Live rock still has bacteria and mini creatures from the ocean. That makes it essential to your tank's health. Dead dry rock is not the same. If you take dead coral based rock and leave in the ocean for a year, it would become liverock. Crabs picking on rock is normal, they are eating algea or copepods too small for us to notice.
live rock grows many of great things, algea (tho not great), copods and types of bacteria that the crabs and snails eat, they will not harm it in any way.