It is a big deal when bracers do not require any proficiencies or abilities to use. To use plate there are a ton of negatives and requirements - heavy armor proficiency, a minimum strength score and disadvantage on stealth checks.
But it is one of three attunement slots, and it is only viable for 4 classes. Again, compare it to the actual same value by itself, which is studded leather armor, which has 9 classes which can use it, no strength requirement and no stealth disadvantage.
This is why the Bracers are so limited, because only the classes that no other choice really want them, and the Barbarian, only if they insist on using a two-handed weapon and have high scores.
Compare that to bracers of defense which ONLY requires attunement, it is far harder to get and use full plate. Plate is only +8 over someone with no dexterity bonus, it is not that in use compared to most that will use the bracers. Plate is only +1 better than a Monk should have at the point a character can afford plate. So a Monk with bracers of defense at a point where plate is appropriate will have a BETTER AC than another character in plate armor with two free hands.
Attunement is an incredibly limited resource. You get three. And yes, it is +8 over someone with zero dex. A necromancer might have a very low dex. A Celestial Soul Sorcerer might have very low Dex. These characters want the Bracers too.
And, to break down your numbers again, if full plate is only +1 better, then you are saying the Monk should have a 17 AC. Now, let's just say that the fighter gets full plate around level 6. Now, the monk can use one of their highly limited attunement slots, with a Rare magical item to jump up higher with a 19 AC. With both hands free.
- The fighter... could have taken the defensive style to get 19 AC. With Both hands free.
- The fighter could have gotten an uncommon attunement item (the cloak of protection) that gives +1 to all their saves and gives them 19 AC. With both hands free.
But, why does both hands free matter? Sure, a shield takes an action to put on, but drawing a weapon is a free-item interaction. So, you could have one hand free to do things like open doors, then draw your weapon as part of your attack. Just about the only thing this prevents is you can't grapple... unless you sheath your sword (which is free) to grapple. So, let us assume the fighter is willing to risk those rare times when having only one-hand is going to be a tricky situation during combat, when AC matters.
- The fighter could wear a shield. This brings them to 20 AC.
- The fighter could get a rare magic item that doesn't require attunement, a +2 shield, that brings their AC to 22
Oh, and lest we forget... most of this stacks. So, you could have a 23 AC fairly easily, with no attunement. 4 points higher than the monk using their attunement.
You also act like any character can use a shield, they can't. The gp cost of a shield is not the barrier to using it, the proficiency is. It is one of the hardest common items for a character to get access to, harder than any other weapons and for most players as difficult as getting heavy armor proficiency. Just about anything else can be picked up with a race or at most one feat, but to get shield proficiency you either need to multiclass into a class that gets it or use TWO feats (one if you already have light armor proficiency).
There are 13 classes in the game.
Natively able to use shields? Artificers, Barbarians, Cleric, Druid, Fighter, Paladin, Ranger (7)
Has a subclass that gives a melee version of the class who can use shields? Bard, Warlock (2)
Has no access to shields outside of multi-classing or Feats? Monk, Rogue, Sorcerer, Wizard (4)
It is actually harder to get martial weapon proficiency or Heavy Armor Proficiency. Just about 75% of all classes can use Shields though. And, on that list with no access outside of feats or the subclass list? Only the Monk, Sorcerer and Wizard need two feats, because the Bard Warlock and Rogue all have light armor proficiency. These three classes also never will attune to Bracers of Defense, because it offers them nothing that they can't get by wearing Studded Leather armor.
If everyone in your party uses a shield like you claim, then many of them took the moderately armored feat because Rogues, Wizards, Sorcerers, etc can't get shield proficiency any other way.
Actually, they are fighters, rangers, paladins, barbarians, ect.
In a typical party you are going to have probably 2-3 characters with shield proficiency. Of those 2-3 characters take out the clerics who are not back liners and need a weapon in 1 hand and another hand free for casting.
Nope, Clerics and Paladins can use their shield as a Holy Symbol, meaning they do not need a free hand for casting per the rules.
Then take out the martials using primarily bows, cross bows and two handed weapons, then take out any that are TWF specialists.
Handcrossbow can be used with a shield, but I will concede that martial ranged characters and TWF specialist
have chosen not to use a shield. Not that they couldn't, they just have made a choice to no use one while using their preferred method of fighting.
Funny thing though? Two Weapon Fighting Feat gives +1 AC, so if they are a fighter wearing full plate? AC 19, just like the Monk with the Bracers.
What you are left with is the characters that both can and have a reason to use a shield, I would argue it is 0 in most parties.
You would be very wrong.
A few probably have a cleric with warcaster or a sword and board fighter, but I think it is a minority of parties that have such a character and very few have 2 of them. Now how many can and would use BOD? Probably 2 or 3 can use them and would use them - all the Monks, most of the wizards, sorcerers and warlocks, some of the Barbarians and Rogues.
Rogues and Warlocks would never use Bracers of Defense, because they get the exact same benefit from wearing Studded Leather armor. Again, to repeat.
To use Bracers of Defense you cannot wear any armor. This is a major drawback of the item. There are 9 classes to whom this item is 100% worthless. That is a super majority of the classes in the game. Only 4 can get any use out of it, one (the barbarian) has to have high stats to even consider it, and the other 3 are where we are talking, wizards, sorcerers, and Monks
You talk about doing something for one subclass; yet in 5 years of playing 5E we have had the same number of bladesingers at my table (3), as we have had PCs of all types that used a shield (1 light cleric, 1 battlemaster fighter, 1 vengence paladin).
So? Bladesinger wizards may be common at your table, but again, if this item is a problem for them, just don't give it to them. But designing this item to be nearly worthless for everyone, just because one subclass can go nuts with it, is a problem.
The issue isn't the item, it is the stacking on top of everything else you are having the bladesinger do.
To put it another way - you say this is no better than a shield and a shield is not a big deal so this is not a big deal ........ if a shield is "no big deal", why doesn't every wizard and sorcerer rock a shield? There is no reason for them not to and certainly every single one of them would take a free +2 to AC? It is a safe bet every one of them with a spare atunement spot would take BOD.
If they could get shields without needing two feats, they would rock shields at every opportunity. But, you said a key phrase here. "with a spare attunement spot".
That is the trick here, is a shield worth attunement? Sure, if you have nothing better to attune to, but how many items are better to attune to? Would you give up a ring of spell storing for a shield? A Wand of Fireballs? There are a lot of things that are far better for them, that also require attunement. And why does this item require attunement when it is already so limited?
This is an item that is better than a shield in combat, does not require an action to don or doff, does not take up you offhand and does not require proficiency. Considering the significant barriers to most characters using a shield, why should this be free to employ? This is better than a shield in use, so certainly there should be some barrier or something to give up to use it!
Finally your entire argument is the +2 AC is not a big deal, if that is true, then you are not losing much if you have to drop it to attune to something else. You can't really have it both ways, either the +2 is a big deal and should require atunement or it isn't and then it is not a big deal if they don't have the +2.
But a smart player sheaths their sword instead of donning and doffing the shield. Most player's don't need both hands all the time. Most players can get proficiency rather trivially with a shield.
And the barrier of being unable to wear armor immediately drops the Bracers down to being usable by 4 classes in the entire game. If shields can be used by 9 classes, and BoD can be used by 4 (one with a asterisk) then... why also make it need attunement? The only reason I don't compare it to studded leather armor is because it stacks with non-armor AC calculations, but if you want to give it to a rogue... it literally has all the benefits of studded leather armor with additional drawbacks and a massive price tag.
I think you are just not seeing how heavily limited this item already is. The only characters whom this item would be a no brainer for without attunement are Monks, Wizards and Sorcerers. And other than the bladesinger, none of them are going to be getting the ridiculous levels of AC that the traditional AC builds can do with magical armor and shields.
The maximum I could see a Monk hitting with this, is if you gave them a Defender, Bracers, two items of Protection, and the Ioun Stone. Max their stats and you could see an AC 28
The max of a Fighter with +3 plate, +3 shield, Defender, two items of protection and the ioun stone is 32.
I might be wrong about the Defender not requiring attunement, but in that case, drop the Ioun stone and both ACs by 1. That is the "worst case" scenarios for both of them stacking as much AC with attunement slots as they can if Bracers are free. Again, a difference of 4 points, not including the defensive fighting style.
There is just nothing the Monk can do with free bracers that breaks anything not already broken. Opening them up doesn't do anything except level the field a tiny bit. And make Bladesingers potentially more broken than they already were.