Great questions! It really depends on the person. While I always wrap my shamisen in a cloth bag (nagafukuro) even in a hard case out of habit, several of my professional shamisen friends in Japan simply put it in the case without the bag. While it’s great for keeping dust off the shamisen outside of a case, there’s no practical reason for it. I do so out of habit and mental discipline, although often ask myself, “Why do I do this??”
Wiping down after use is a good idea, as oil and grime from the hands/fingers can build up on the sao. (Any microfiber cloth or even a soft shirt can work.) Removing the koma is also good, as it relieves tension from the strings and the koma, so both will last longer.
I have a little article on basic care written here. Nothing too special but it might be useful. - Caring for your Shamisen