The idea about classes getting their own 5 new abilities seems okay, but then you essentially have a job class that can use any ability from any class, and thus jobs will be at a disadvantage. ex a pugilist with job like abilities but can still use cure.

It's doable I guess, but it would be a pain to balance.

Just leave it like it is. The system is pretty good, we just need more jobs to branch from. If you get rid of classes you also have to rethink the entire leveling system. Personally I'd rather just level a hand full of classes and then do content to branch into jobs, than have to level up every job by itself.