You're kidding, right?! Please tell me you're kidding. Seriously...
If you count as "diversity" whether the effect of your spell is blue (ice) or red (fire) or purple (lightning) or whatever...then what stops healing to be as diverse?!
There's phoenix (the most powerful healing power in all of final fantasy games is the FFVII I believe Phoenix...full party heal and revive with big-ass damage to the enemy party), so clearly fire can be used to heal. Wind and water both are traditional healing elements. Then there's holy because...you know...holiness and healing go hand in hand. Gaia, the loving mother earth, is often represented as restoring strength...so we can use earth as healing element as well. Dark arts are used for just about anything under the sun...for the right price. So add that to the bag. Then there are natural energies like KI, Chakra (Final Fantasy Tactics had monks with a good non-magical healing skill...called Chakra...and even a free revive skill). Then there's also the good old-fashioned medicine. You can also "reverse time" to unwind wounds or cheat life and body with "real" illusions.
There are TONS of means of showing healing thematically as shown above. Those are not all even. You could find tons of them.
And you are missing a massive thing. Healers ALSO DPS...Even if their healing would be the same, the manner in which they attack can be different.
Or maybe you are talking about mechanical variety?! Then healing is exactly the same as DPS. Burst healing, healing over time, health drain, max and current HP cap increase. You can also add shields as a de-facto healing. Damage is the same. Even if the animation and weapon changes, there's just so many ways it can happen. Ultimate it's just numbers that are detracted from bigger numbers.
As for the topic, healers need a HIGH PROFILE class to be added. Dancer just happens to be a high profile class. It needs a class that will make players want to try healing with it. If Dancer wouldn't be a healer, they'd be high-pressed for another class. Because no, I do not think that Chemist or Geomancer fit the bill. The former is the most basic healing class from Final Fantasy games that you don't use after the first few missions in general, while all the "rave" for geomancer began only with Stormblood, even though there were mentions of it before it.