No, it won’t. THP = HP.
I don't understand what you mean here. THP and HP both spend the same. A 10th-level bladesinger with 62hps and 26Thps can take more damage than the 10th level fighter with 84hps.
Only if your DM is putting in effort to make it so, or not challenging the party with actually threatening enemies, like enemies that aren’t all at the lowest possible end of to-hit for thier CR.
Math is involved here. Even if you assume AC is equal, hits by an enemy that will do the same damage to a character with less total hps will kill that character faster.
If you crit a 10th level fighter with 84 hps for 90 damage that fighter goes down, if you crit the same bladesinger standing next to her who has 62hp and 26THPs and she reduces that damage by 20 with a 4th level slot she does not go down. At this point she still has 16hps left and is still standing even with a crit that would have taken the fighter to 0 outright. If someone comes in and casts mass cure wounds for 20hps the fighter is back up with 20 and the bladesinger has 36.
Now that assumes you crit and assumes the chance of critting is the same. This is not actually true, it is generally going to be harder to crit the bladesinger and it is going to be harder to hit her too, meaning she has likely lost less before that hit, but for the moment we will ignore that.
If you use the same example and it is 91 damage ancient red dragon breath, again the fighter goes down unless he can cast absorb elements as an EK or make a near-impossible dex save. The bladesinger (who has a better chance to save even without indomitable) casts absorb elements, loses all her temp hit points and has 43hps left. Even if the fighter makes his save or casts AE he is still at a lower hp total.
If it is a green dragon breathes on them for 77, the fighter has 7 left, the bladesinger has 11. The bladesinger doesn't even need to use a spell slot to stay up (although she can and will have even more hps if she does).
Now you can say she used her reaction on the first two and there are more attacks coming and they are going to overwhlem her. Sure that is viable, but regardless of how you slice it she has more hit points and is generally going to be better able to take other future attacks this round than the fighter standing next to her. If he gets to cast 2nd wind he can even it up, assuming he has not done that yet since his last long rest ...... and assuming he is conscious when his turn comes around.
There is just so much missing here. Your Bladesinger tank is successful because of your group’s playstyle, and adherence to rather weak encounter design. I don’t mean that as in “your skills are weak”, but as in “the encounters are weak”. CR 13 with +8 to hit? Really!? No wonder you overvalue the +3 to +5 to AC compared to Hide armor from Bladesong.
I am currently playing in 9 different games (2 as DM, 7 as player) to include 5 games on roll 20 being played with people throughout the world.
According to the DMG p274, +8 is the normal attack value for CR13. There are presumably CR13 with both higher and lower attack bonuses, but that is the nominal value for CR13 RAW and that is what I was quoting when I said that.
Regardless of what the attack bonus is though, it will always be more difficult to hit a higher AC and more difficult still with disadvantage, and will be 1/20th as likely to crit with disadvantage. No matter how high the attack bonus is those things are always true for an enemy that makes attacks and has a crit range of 20.
You brush off threats that aren’t AC or elemental as if they just don’t matter, but in my games and the games I’ve watched and heard about and played in, those threats are often what threatens the group the most. I've rarely seen a TPK close call from enemies who mostly just attack against AC.
I understand that, see the green dragon example above.
But also to be clear, after 10th level the bladesinger can reduce ANY damage as long as she is in bladesong and with false life she can start the fight with as many hit points as a D10 martial, she is ahead at the start of the fight, gets hit less, and loses less hps when she is damaged. It is math.
You say I am brushing off threats that are not AC or elemental. Threats that cause damage can be reduced through SOD, even if they are not attacks and not elemental. Certainly that is not efficient and not optimal, but most other characters, to include most raging barbarians, can't reduce most of those non-attack/non-elemental damage types at all. Threats that are not attacks but cause debilitating conditions most often require a Wisdom or Dex save. She is proficient in wisdom saves and has a decent dex save. Both of these saves are better than most other tank builds. So while non-attacks and non-elemental damage can be challanging both for the party and for the bladesinger, the bladesinger is generally as well equipped to handle it as most other characters.
Additionally, you’ve noted that you don’t think Bladesingers are that good at offense. So, why on earth are enemies not just walking past or around the BS to hit targets that are actually wrecking them and their friends?
Many reasons, chokepoints and movement limit being the two most obvious and common. It is not like it does not happen though. Regardless of who is in the front tanking, intelligent enemies are going to try to get to squishier characters.
You’ve talked about playstyle stuff as if it’s numerically objective a lot, like with the familiar.
It is a familiar and has 1 hit point. It will be killed by any AOE at all and it has limited movement.
Most DMs IME don’t waste enemies attacks on the familiar unless the familiar has been boosted in some way. An owl with dragon’s breath will last several rounds IME, dealing significant damage in a fight against a large number of enemies.
That is because most DMs do not play enemies smart. Most of the time it is generally advisable to take out your weakest foe first if you can. That is particularly true of a familiar flying around breathing dragon breath.
I do know that a lot of DMs don't do this intentionally, but that is because they do not play enemies smart. If you are not using the familiar that is one thing. If you are using him to breath fire every turn or help the Rogue so he gets advantage every turn it is stupid to let him stay on the battlefield when he can be easily removed in one attack. Sure there is an opportunity cost to this, but it is a heck of a lot less costly than letting the Rogue have advantage every turn or worse having multiple people taking breath weapon damage every turn.
Unless you are going to down the PC this turn, it is generally less advisable to attack a PC than an active familiar that you can easily take off the board this turn. This is especially true when you consider a familiar dropped to 0 can not be revived. If you whack the Rogue and manage to take him to 0, there is a significant chance he will be back in the fight on his turn, the familiar is gone for good if you hit him at all.
Now if the familiar is not doing anything that is a different story.