I Think It'd Be Batman Because Of His Father Instincts - Tumblr Posts

I imagine that Billy can sleep anywhere without problems because he has been homeless for so long he just naturally gained the skill. He has slept under bridges, on the ground, under desks, on chairs, and in the park.

He even slept in the zoo with Tawky Tawny which was the most comfortable sleep he's gotten (all curled up tigers!) but was dangerous because he was almost found by the zookeepers!

Captain Marvel doesn't need sleep but imagine Cap doing the same after a big fight, he just puts his head on a small desk in a uncomfortable angle and passes out. Everyone around doesn't know if they should wake him up to tell him about the staff rooms or just leave him there to get some sleep.