Also take into consideration that a lot of the bigger fights you'll be doing at lvl 50+ and outside of Light party dungeons will have an enrage timer. This means that if the DPS of the raid doesn't kill the boss before X amount of time, the party will wipe. In those cases, healer DPS can be very valuable.

On top of that, every healer class has a way to manage their MP consumption and regeneration. White Mage has Shroud and Assize, which they can use around 5 to 7 times in a 10 minute fight. If you have a Bard or Machinist, they can aid your MP recovery if you're running too low from raising people, and no one has ever said you're not allowed to use Hi-Elixirs during battle. MP management and DPSing is something you will learn to weave into the skillset of a healer, so don't dwell too much on it, it will come with time and practice.