Could the governed enforce a ban on Superheroes in Marvel/DC?

As the title says if heroes were banned in the Marvel/DC universe like in The Incredibles, could the government enforce it? Would the public support it? And if there was a syndrome-like figure that hated Batman/Iron Man, could they kill the heroes in the same manner without anyone noticing?

I always found it so interesting how Syndrome could take don't all of Earth's main heroes. Especially the way he went about and the circumstance that allowed it to happen. So, if the DC or Marvel universe successful ban heroes could a villain like Syndrome pick them off? If so, what character do you think could succeed in such a task.