Except that

1. That would be ANOTHER DEX class.
2. Eliminates healer ability to sprint.
3. TP is a much different resource than MP since it recovers 6% per tick in combat. So unless you make all the skills cost 70+ TP they could have infinite healing (especially with downtime, especially since unlike DPS you don't have a healing rotation of some sort). And then you'd have healers asking for Goad.
4. By linking DEX to healing, you give them an unfair advantage in that they are the only healer that doesn't require Cleric Stance and thus doesn't have to gimp their heals to DPS or vice versa, whereas healers use two different stats (INT and MND) to dictate their performance.
5. No beneficial party bonus for the other healer

There would be so many balance issues with something like that