Blade singers already have a busy bonus action though. Activating bladesong takes your bonus action, and so do many spells.
I like Bladesingers the way they are. Extra Attack synergizes nicely with Athletics Expertise for Roguesingers. It gives you a cheap melee control option which is also fun in roleplaying scenes so that you can, for example, grab an NPC bully by a small joint and kick his feet out from under him so that he winds up with his chin on the ground and unable to get up. Without Extra Attack that would take multiple turns of scuffling, but with Extra Attack the Roguesinger can do it in a single action.