If every job receives the ability to raise, then making health bars go up should return to being the sole purview of the healer role.

The reason healing was given to everyone else is to lessen the burden on the healer role, so if everyone can raise a dead healer, then this advantage isn't required anymore.

Giving jobs like the tanks the ability to raise and allowing them to keep the ability to heal would not result in balance, it would just be propping up the importance of one role over all the others. Balance means every role in the party having their own importance, if you remove one advantage entirely from a role, you need to give them another to replace it.