Some jobs can do things other jobs can't. That's normal and expected. That's why we have 17(?) jobs and 4 roles to choose from. We don't need to make every job feel the same in AOE pulls.
As for why we don't remove MP, probably because it's convenient to keep it. It's mostly a resource for healers and BLMs to manage, but other jobs dip into the MP pool as well because, why not? It's there and it makes sense in terms of lore and job flavor. It's not like they are going to remove the MP bar when you switch jobs. It wouldn't make sense to remove it since all current and future healers are going to use the bar and it can be used as a restriction on any number of things in the future (like BLM spells and raises).