The floor panels are usually of a marine grade ply wood and they have been pressure treated with wood preservative. By painting them you will seal in any moisture in the wood and accelerate the deterioration process.
Auminium chassis don't need paint either as they oxidise slightly over time which again is their natural anti corrosion process. Aluminium does "age harden" so do by all means keep an eye out for cracks. Swift in the 80's had a spot of bother with this. I must say that in recent years I've not heard of any major issues.
Steve L.