Okay, blaming myself I said "they're in combat for 5 rounds - they're tanking while their allies deliver lethal".
My bad, you did say that, but then that analysis is silly -- the odds the tank would need to do so against that kind of creature is very small, especially given a single level has the fighter killing the creatures solo without dying while the bladesinger always dies.
So, then, if we look at more realistic scenarios of only needed to tank the creature for two rounds or so, the fighter always survives barring 3 or more crits while the bladesinger dies outright (not dying, straight to dead, do not collect 3 death saves) from a single crit. This puts the odds of the bladesinger dying in 2 rounds at about 19% (4 attacks at 5% cumulative chance of crit), while the fighter chance of death is equal to getting at least 2 crits in 4 attacks or 10%. The bladesinger has about twice the chance of death of the fighter in this scenario.
We (hopefully) agree on that last: however much critical hits are a danger for BS, Champion is even more screwed. Battlemaster has more options, such as Menace... but we'll come to that.
No, because a crit kills the bladesinger outright whereas the Champion has a decent likelihood of surviving the encounter with his party. If you want to bring in party play, you need to consider it all around -- the Champion tank has a far higher chance of surviving multiple combats as the tank because he's not susceptible to one-shot death.
For me, the footprints in the butter lead clearly to "What the heck, how is a Wizard tanking in the first place!?"
With an extremely high level of risk of outright death. Seems a fair trade.
So here I believe we agree on the premise but disagree on conclusions. For me, the fact that Wizard hugely overshadows Fighters is a reason to not give Wizards any more toys! Especially, not toys that step on fighter toes (Battlemaster or not, being able to cast Fly and Fireball etc beats it.) And most especially do I not want to see an AC 23 (28 with Shield) Wizard flying about, with advantage on Acrobatics and +Int to their Concentration saves, bopping foes with GFB or BB, and up and up and away again. Did I mention that they can land, use their freebie extra 10' walking, then go back to flying?
Their only downside is possessing a strong odour of fromage!
(From, Mage! Cheese... you see what I did there?)
No, because, again, the bladesinger is either being a wizard, which does wizardly overshadowing, or being a risky tank, but not both at the same time. The opportunity cost for not being a wizard while you're a mediocre damage, very risky tank is enough that the bladesinger doesn't effectively become an uber wizard in the game. A similar analysis of the Mystic Theurge from 3.x had similar screaming of overpowered, but it turns out the choice to be a cleric or a wizard round to round wasn't overpowered, in fact it was a tad underpowered but very flexible. The bladesinger is similar -- the first blush is a reaction similar to yours but that actual play is fraught with choosing to be a wizard and blasting or jumping into melee and being rather mediocre about it. The trade off means that it's not either at a high degree of effectiveness.
The high AC possible from a high rolled stats for a tier 1 bladesinger is quickly eroded in usefulness as you level into tiers II and III. By tier III, that high possible AC isn't much of a factor given the very low hp pool of wizards. Sure, it looks awesome in tier I, but a lucky crit will outright kill a bladesinger. Going into melee with a 5% chance per attack of outright death when fully fresh isn't overpowered in any way -- it's high risk high reward.