Multi-cellular organisms that move need a nervous system. Furthermore, they tend to develop actual neural masses of nerve cell networks. In contrast, primarily immobile multi-cellular organisms (i.e. plants), don’t bother with this brain game. They save the energy of growing and maintaining a modal nervous system network, as apparently it’s not beneficial enough for their lifestyle.
Interestingly, there is a sea worm which has a two phase life cycle: it will swim/squirm around in it’s early life then settle into an immobile state. The first thing it does after committing to still-life is digest it’s brain.