First, let it be said that I am NOT a good housekeeper. I clean when I have to, not when I should, using a sliding scale from "untidy" to sometimes close to "Gag! - clean this NOW!" When food falls on the floor, the dogs get to clean it up first, then I scrub that spot afterwards.
But my bathroom has a tile floor. Real tile. No bathtub, just a shower stall. The brooder is in the bathroom. I do not cover it. When the chicks learn how to get out of it, I just clean up after them. It's only chicken poop, not dog poop or elephant poop, for god's sake. (It's actually less nasty than when I had to clean what my various former husbands did to the OUTSIDE of the toilet.)
I cheer the chicks on when they're learning how to fly to the brooder's edge. I congratulate 'em when they make it out and wander around in the bathroom. And cheer even more when they figure out how to fly back INTO the brooder.
Granted, I've never had more than 7 in the brooder at a time; usually it's just four or five or six at a time. Also, I struggled with my relaxed attitude when I got two ducklings... oh lordy, they needed higher walls on that brooder!!! Good thing they go outside younger than chicks do!
So I think it's adorable when chicks get out of brooders. That's just me. I think I was an indulgent auntie, too.....