It's more relevant if you are using Blur, as the +1 AC really helps. By level 5 you are expecting foes with +3 to +6. With 19 AC they hit with 1:4 to 2:5 of their attacks. With 20 they hit with 1:5 to 7:20 of their attacks. That is magnified by Shield of Faith and Disadvantage, so that they start hitting with only 1:100 to 1:16 of their attacks. In conjunction with the relatively low number of attacks that each foe is likely to get per combat, forcing* that one value tails incoming hits off dramatically. I like your use of Warcaster a great deal - it looks very satisfying! Taking the Feat instead of the ASI means committing to a high resource-use character, so there's the downside.
My principle critique could be restated as "don't make casters that overshadow martials". Strongest defensive toe-to-toe character should be the one with plate, shield and Defense fighting style. Wizard already has the most toys: they don't need this. Some commentators have focused on a single dimension of that critique, to suggest that if BS can't also do wizardry then there is no problem. That single dimension isn't the only dimension of the critique, which is more concerned about Wizards stretching out to overshadow martials than whether BS is the strongest Arcane Tradition (I believe BS is top-two, that said). However, even looking at that one dimension, the framing under which it could make sense requires us to ignore the efficiency of Blur + very high AC. Proactively using Mage Armor (runs 8 hours, no Concentration) + Blur (Concentration, 1 minute) + Shield of Faith (bonus action to cast, Concentration, 10 minutes) with Bladesong ends up saving resources over the course of the combat.
Then, because we spent 1/6th of a 1st level slot + a 2nd level slot + a 1st level slot, with likely 1-2 heals and 0-1 Shields on top, most of our 3rd level slots (and higher) wind up free for all the wizardry our hearts could desire. Worst case, BS simply switches roles. Other Arcane Traditions don't do better than this, because they still need to cast something each combat. So even though I don't believe my critique can be rebuked solely on that single dimension (it's wizard overshadowing martials that I excoriate) I also don't believe that a very strong case has been made to show that BS can't do wizardry. Sitting at the table next to our guy in TotYP, I'm seeing plenty of CC and AoE output on top of his BSing. Still, we're only a few sessions in.
*A feature of the mechanics of RPGs is that balancing faults often arise from forcing a value. From a professional expertise perspective, that is part of what makes adding Int to AC egregious, because the designer should have looked at that forcing with concern. Overshadow and power-creep then rear their ugly heads. I should add that averaging damage instead of playing out scenarios might fail to explicate such a forcing because it is representing damage as coming in constantly, when really that damage is arriving infrequently and in parcels.
Right, you're using 1 first to set up your day, and then 1-2 firsts and a second from the bladesinger and a 1st from another caster (potentially a 2nd if you're using warding bond) for
each fight. At 4 fights a day, you're now using higher level slots to fuel shields and blurs, and you've tapped your cleric of all first level slots just to
enable your melee actions.
Let me put that another way: in a 4 fight day, you're burning 4 2nd level slots and potentially 1-8 slots on shield, and the cleric is burning 4 1st slots on shield of faith. NONE of these spells are draining resources from your foes -- no damage, no lockdown, no area denial -- they're ALL just to enable a wizard to have a high survivability in melee. And you claim this isn't a huge investment just to enable a wizard to not be hit and doesn't affect that wizard's ability (or their party's) to accomplish things? If you're using your much rarely 3rd+ slots for exploration and social encounters then you've already sacrificed a huge amount of the wizard's versatility because a lot of obstacle removal/bypassing is in those 1st to 2nd level spells.
And, further, I did my math wrong. In your Hill Giant fight you presented eariler, you took 8 rounds to kill the hill giants. If one (and only one) is attacking you every round (as tank) in melee, then the chances to be hit are:
Not hit at all: 22%
Hit at least once: 78%
Hit at least twice: 43%
Hit at least three times: 17%
Hit at least four times: 5%
Crit at least once: 4%
This is assuming usage of blur as per the scenario. That's 2 attacks a round by 1 giant for 8 rounds for 3d8+5 damage against a hit point pool of 36 hp. It's very likely you will use 1 shield, and pretty likely you will use 2. So, even if you look at discrete chances and don't average, the bladesinger actually comes off worse, not better.
If you'd rather an easier fight, say where the bladesinger is tanking 2 giants for 2 rounds, the numbers aren't that much better:
53% chance to be hit at least once
17% chance to be hit at least twice
And that's out of only 8 attacks. Again, assuming AC 23 and blur.
You're burning a huge amount of resources to enable your trick of having a high AC. And the comment that the casters will be casting spells in combat anyway is ignoring that they'll be casting spells to harm/delay/remove opponents, not enable the bladesinger to act the tank. The spells being cast will be directly contributing to ending the encounter, not to let the bladesinger stand in the way of melee.
So, yeah, you can burn a heap of resources and be less hittable than a fighter. That's not overshadowing, it's burning a huge amount of resources to be a bit better at not getting hit. When you are hit, it doesn't help at all.