I was always told if you caulk to leave the back open so leaks and smells can be noticed. So, it’s mostly for looks. Some local codes might require it though, so check if your local code was amended.

I have seen aquarium sealant (pure silicone, the clear stuff that smells like vinegar) be used around the flange to seal up any gap between the flooring and the closet flange which prevents leaks from wetting the subflooring and causing it to rot out.

If you have an uneven floor (bad tiles/old house etc) and you don’t trust shims to hold forever, you can also seat the toilet on plaster of Paris; just leave the back open so leaks can’t build up but again this is only necessary in unusual cases.

TLDR; if you don’t prefer the look and it’s not a code requirement and you are confident that you can achieve a solid mount, you can skip it.