FormerlyHemlock
Hero
Multi-class slows spell progression.
How do I think it's overpowered? OK I'll take my character for example at level 8.
+2 studded leather with an 18 in both DEX and INT. He has a natural AC of 17, bladesong 21, shield, 26. I reserve all 4 1st lvl slots for shield, and 2nd lvl if the need arises (never actually happened). I do have mirror image and blink, neither requires concentration which means I can make it impossible to hit me, or even target me. If need be I can also stack protection from evil and good to give disadvantage to the rolls. In other words, I have no problem in melee combat. I do have offensive spells if the need arises to sit back and not melee, but why do that when it's so much fun frustrating the DM who can't hit you? BTW my sword attacks do 1d8+5 each, which isn't too bad.
AC 21 with Bladesong (with Shield on tap) isn't an outlier. A pure Eldritch Knight can do exactly the same thing with Defense Style, except he has AC 21 all the time, including before his first round of combat. A Paladorc (e.g. Paladin 6/Sorcerer 2) would have an AC of 23 at level 8, right on the verge of being able to cast Quickened Mirror Image/Blur/Web if he needs it.
The theoretical advantage on a Bladesinger over the Paladorc is that he's got access to more and better wizard spells, but if you're saving all of your spell slots for defensive use it winds up not being much different in practice.
BTW, an 8th level Necromancer will dominate both the Paladorc and the Bladesinger. 30 skeleton archers = 30 attacks at +4 for d6+5 damage each. Likely to be 120-160 points of damage per round against idiomatic/level-appropriate foes. (Not that I believe in "level-appropriate" anything in the first place.) Even against an adult white dragon it would still be 94 points of damage per round (only 31/round if the skeletons are at disadvantage due to fear or at long range).
Therefore, as a DM, the Bladesinger doesn't even impress me, let alone cause indigestation. It's not even an outlier in terms of the PCs I am prepared to deal with.