The reason why most house rabbits here don’t have sawdust is primarily that it’s much easier to litter-train and maintain good bathroom habits if there’s sawdust (or wood stove pellets, carefresh or Yesterday’s News etc) in the litter-box(es) only. I recommend fleece-blankies (or pieces of) on the floor, because bunnies need sth to dig in and drag around etc. Fleece doesn’t have threads like towels and ragrugs do, so it’s safer, if the bunny should happen to ingest some.

Another reason for not having sawdust in a cage is because it tends to get stuck in a bunny’s fur, esp if you have a long-haired breed, and it makes a mess on the floor outside the cage. As for hay, if you put hay on the cage floor the bunny may pee and poop on it, and then eat it, which is not good. So it’s better to keep hay in a hay-rack or in a hay-ball etc or in a bowl or well, any other place than where the bunny likes to go to the bathroom.

In all honesty we didn’t put anything in Rosies cage. At first we did newspaper but once she started using the litter box only we stopped putting anything but a sprinkle of hay in her cage and thats it. She’s free roaming the house so I don’t feel like she needs anything in there right now. However we have a nice hay mat for her that she lays on a lot when she’s in there.