Aside from a complete overhaul like that not sitting well with a lot of existing players, there are some balance issues.

Tank duties are difficult to share against single bosses without adds. Two DPS classes with tank sub-role are likely to perform worse in tanking than a single pure tank class. Already in many trials and non-alliance raids the second tank is basically just a bad DPS. Tank swapping is a valid mechanic but may be too difficult for most players. On the other hand if content is balanced so that a single tank sub-role is sufficient, it will make pure tanks superfluous.

Crowd control will easily be either an absolute necessity or completely superfluous. For trash enemies and weak adds it's generally better to have more DPS. If bosses or strong adds can be crowd controlled, it easily trivializes the entire fight to the point where you don't need a tank at all, and possibly not a healer either. Most existing classes have a stun or two but those are so minor they do not constitute even a sub-role.

The value of a pure support role is highly dependent on party size. If you swap out one DPS of a 4-player party for a support, the buffs and debuffs they give out would have to increase damage output by around 50% to break even. Do the same in an 8-player party and the net result is a 25% increase in damage. A support sub-role already exists in the form of AST's cards, which are easier to balance thanks to a healer not dealing so much damage in the first place. They are also an important thematic element of the class and it wouldn't really make sense to swap them out for some other sub-role.