The surface on the inside doesn't need to be painted, however, from a cosmetic point of view, it may be desiable to some(?).
The drive may have a little water coming in and building up over time, perfectly normal per drive manufacturers instructions. It should never fill up of course. If you think of the drive as a second bilge, it will be seen as such, unless your bilge is bone dry.
Check seasonally, and measure how much water comes out so you can record how rate is increasing and when it demands attention.
Never get rid of the foam block even if it is partially wet. Leave it alone.
If you have too much water buildup and looking for the leak, for drives with the blocks, take off the upper most cover and fill drive with garden hose on a clear day in the morning, look for where the water is dripping out by end of day, if not wait several days, it will eventually leak.
No reason to throw the baby out with the bath water, the drive's life is the same as hull, just maintain it and keep the zincs doing their job, same way they protect your motor made of the same alloys.
My drive has a leak across the top horizontal joint of the drive at the hull seam, I see now why, the flange is very small up there. I hear it hissing as the sun heats up the drive. Very little water accumulates, so I could care less.