Myself, a Fighter 11/BS 6 is free to make 2 attacks and a cantrip as part of the attack action. It is T3 and you built your character for just this trick. Have fun. I don't see a serious balance hit here, nor is the wording so tortorous I'd recoil.
I'd also say that Haste is "the only thing you can do is one single attack in the attack action", which bars making a cantrip attack in the hasted action. Haste is already pretty darn strong, it doesn't need the boost.
Thank you for elaborating the different readings. That is exactly what I thought about. I do think the most RAW way is either 3 attacks or 2 and a cabtrip.
Probably if you allow 3 attack + 1 bonus action attack as a fighter, bladesinger they can then make 4 attacks with 1 of them a cantrip... which seems more than a level 20 eldritch knight can have and about equal to what a level 17 warlock can do.
So I think I would lean to that you need to decide.
On the haste case, it states one weapon attack only, while the normal attack action only states you make one ranged or weapon attack, which can encompass attacks that are from spells... which I actually just noticed...
So I would lean to not allowing the bladesinger to cast a cantrip there.
On the other hand, i have not seen a ranged attack or melee attack that is not a weapon attack which is triggered by using the attack action.
Edit: on yet another hand, the special action granted by the healer feat is usually interpreted as use an item action, which can be done with a bonus action by the thief subclass.
Using the same logic here, hurling a produced flame (you already had in hand) or using a flame blade could be ruled to work together with extra attack...
Edit:
On the 4th hand, the use an object action states, that everytime an item say it takes an action, that it is the use of "use an object" probably a magical flame is use a magical object?
I have afound a single case, where you are allowed to use a spell attack with your attack action: the sunsoul monk special attack.
