This is done using two limited resources. You can hit this AC exactly seven times a day, in encounters you have Bladesong up, and at the expense of being a wizard in any other meaningful way. The EK fighter is sitting at a base 20 all the time (21 with defensive style) and can do this 3 times a day, giving up only a little of their shtick to do it.
Wait until you realize that at 4th level, you can rock a 20AC with disadvantage to attackers by using blur, 3 fights a day, and still peak up to 25 AC 4 times.
This really isn't a problem because the Bladesinger is spending all of their resources to do something a Fighter mostly does without effort, so they're not being the Wizard, just a dodgy fighter. The Bladesinger is much better used as a Wizard that can survive melee rather than a melee combatant that's occasionally a wizard. The lack of hp and poor saves vs CON and DEX mean that a lot of things really hammer a Bladesinger on the front lines. What's really killer is a foe that just knocks the Bladesinger prone, because AC and blur don't help with that at all, nor does Bladesong. Two enemies that knock prone and grapple make the Bladesinger easy prey for anyone else, and it's unlikely they'll have an easy time escaping -- even if they do, they aren't doing anything else.