Mattresses are perfectly fine just sitting on the floor.
... for a while. Used this way for prolonged periods without airing and drying usually means that the mattress accumulates moisture that never goes anywhere. Which gets rather nasty after a few months, at least the cheap foam mattress type does. Been there, done that - but this was with a cheap foam mattress. A spring mattress is probably a lot less prone to this happening. Or you just could start airing them after a week or two of continuous use.