Sure. But when are you taking that. Anytime before level 7 and you've delayed your extra attack.
Anytime after and you are delaying super valuable higher level spell slots.
I'm fine with that assumption. It's even easier to balance out pre-level 11 than post level 11.
I'm sticking to the bladesinger comparison and it's just not true. Like even in a single encounter 4 round day it's going to go something like this.
Comparison
Level 7 Bladesinger (precasted mage armor/and a level 3 false life)
- Turn 1: Bonus Action Blade Song. Action Cast Conjure Minor Elemental. Reaction Shield Spell.
- Turn 2: Attack action for ~23.7 DPR. Reaction Shield Spell.
- Turn 3: Attack action for ~23.7 DPR. Reaction Shield Spell.
- Turn 4: Attack action for ~23.7 DPR. Reaction Shield Spell.
HP: ~63 (including temp hp, +3 con)
AC: ~24 (with shield spell, mage armor and +2 dex, +4 int)
Damage: ~71.1
Level 7 EK (precasted level 2 false life)
- Turn 1: Bonus Action Magic Weapon. Attack action (Greatsword, Graze Mastery, GWM and +2 Str). Action Surge Attack Action. ~49.6 DPR. Reaction Shield Spell.
- Turn 2: Attack action for ~24.8 DPR. Bonus Action Second Wind. Reaction Shield Spell.
- Turn 3: Attack action for ~24.8 DPR. Bonus Action Second Wind. Reaction Shield Spell.
- Turn 4: Attack action for ~24.8 DPR. Reaction Shield Spell.
HP: ~95 (including temp hp and 2 Second wind uses, +3 con)
AC: ~24 (with shield spell, full plate, defensive fighting style)
Damage: ~124
Conclusion
For this short adventuring day (a context we usually consider full casters being better for)
The EK does ~74% more damage and has ~51% more hp.