Yeah that is the reason I have honestly move twords the bladesinger and away from the eldritch knight if I want to use a sword and cast spells. Just get elven chainmail as a magical light armor and the look is complete. You can make 1 sword attack and cast booming blade or green flame blade as part of the same action at 6th level, if you have activated your bladesong then your ac is as high as fighter. You don't have the fighting style or action surge but that is a small price to pay for access to haste and fireball by 5th level and both of those can be easily gained with a small fighter dip and my spell casting will still be better than the eldritch knight.Yeah waiting till high level for fireball and haste sucks tbh.
I wish they’d try to make partial casters gain spell levels at the same levels as full casters, and just progress spells slots more slowly.
Honestly a fighter 1/wizard (bladesinger) 6 is hands down better in my opinion than at fighter (eldritch knight) 7 unless they make serious enhancement to the archetype. It is not that bladesinger is to powerful in my opinion but that the eldritch knight is just so inferior to this or a valar or sword bard.
I don't look at hexblade or paladins because they behave so differently in my opinion.