I use
Wipe Clean Tuffies mainly. My allergic boy has one in his crate which I sling a cotton towel over. He uses the towel variously as a cover/pillow/scrunch thing, depending on his mood. I have used towelling cot sheets too but he prefers something he can move!
I have Orvis cotton canvas covers on the Tuffies in the living areas. I also have an Orvis memory foam bed in the hall which they use quite often.
One of my dogs has a dog duvet thingy in his bed which he adores - looks like the princess and the pea bed, as we bunged it on top of another waterproof pad and a spare pillow :) His is a bit hot and can get whiffy more quickly
My utility room smells like a boys locker room each morning, summer or winter. The advantage of a Tuffie is that they don't hold the smell and the towels can easily be aired or washed. I know plenty of dogs that are happy without covers but mine are peculiar...