I think it'd be a mistake to make a bunch of other healing classes that heal as WELL as White Mage, while also having a utility beyond just the healing. We've all stated that White Mage does one thing: it heals. The last thing it needs is Chemist walking up into its territory and smacking it down off the hill, because Chemist heals just AS WELL, but Chemist also debuffs the mob. Balance is going to be a very key component to any new jobs that get added.
I think to reach that balance, you have to look at synergy. The classes need to cooperate to be stronger together, where they'd be weaker without one another. For example: Chemist comes out as a class. It has healing abilities, but these healing abilities don't quite reach the playing field of the White Mage. What the Chemist does have, however, are great buffs and debuffs. Chemist could use an Area of Effect potion that will amplify the next Curaga delivered, which only the White Mage can do, or a buff potion that will allow the next target buff (like Regen) to last a certain % longer. They're not the same jobs (and Chemist could do it all by itself, albeit a little less effectively), but they're designed to amplify each other. Imagine the Chemist popping a potion that allows it to absorb Regen up to a certain %, with that extra % of HP then transferring to another party member on the next target potion used.
This synergy can be applied to any class archetype. Damage Dealer, for instance. Maybe Samurai comes out with a plethora of armor debuffs (or an armor debuff is the natural effect of its weapon skill combo) that allow the Monk's next attacks to be more effective, or act as a guaranteed critical for the Dragoon. Dragoon has its lance for armor piercing, but the other DD classes could always benefit with some extra help in that regard.
Postulation is really as far as we can go at this point. We don't know the content, the situations, or the other variables we're going to be faced with. I just think that we don't need different options in terms of "I want to take a Chemist healer today", but options in terms of getting the most out of the classes offered. In the end, the community is ALWAYS going to do what it wants. It's going to demand that its way is right and that everyone else follow along, like it did with Ninja, Red Mage, and Summoner (to name a few) in FFXI. SE can prevent this by making each class benefit the other, without taking some of X job's toys and giving them to Z.