That's a fine concept for a Healer, and in this game Healers are the closest we have to Healer/DPS hybrids given they already do DPS as part of their kit (gutted as it may be).

But it wouldn't be a real hybrid, Red Mage is already suffering because of some weird "it's a hybrid!" fantasy. It would be a healer end of the day. A magical melee DPS would hopefully still have room to exist.