Yes, I removed the mattress parts and place stuff up there based on it’s probability of staying safe. I use sheets of the waffle-like shelf liner (actually it also looks like rug pad) in areas where more friction is needed. I have never had problems. My overhead has a rough finish so that is very helpful also. I am old and not too strong so nothing very heavy goes up there. It is an extremely useful area.
Some things, like my banjo, ride on my bed and then get moved overhead when we arrive.