It is not enough to make all healing/support classes options. If you want to enable styles of play where they are highly useful additions to the party and also support styles of play where they are not necessary--to do many of the traditional things that people do with D&D (whatever one may personally think of those things)--then you need some optional healing rules to go with that playstyle choice.
Otherwise, a dedicated healer that is either providing abilities that aren't really needed--and thus will feel even more useless than otherwise, or is absolutely necessary. If the latter, then a healer that isn't dedicated can't carry the load. You can't have both with a single set of healing mechanics.
If you look at the big picture while trying to balance the issue, you're probably right: either healing is necessary and nobody will be able to go without it, or getting a healer is an option, but if it's not really necessary, why don't we go with another warrior type and increase our offensive power?
Personally, though, I prefer to analyze it using a case by case method. For example, let's take another feature that appears in some classes and not others, that is, the ability to thrive in wilderness environments. Barbarians, rangers and druids have a sweet spot here, but a group of fighter, paladin and cleric running through the same adventure would probably have an increased difficult, while they actually have the same types (two warriors, one priest).
I'd like healing to go from a feature that every party is supposed to have to one like the ability to survive in the wilderness: something that may be seen as crucial in a given party combination or adventure setup, but not so much in others.
In the game I'm currently developing, I'm having a hard time trying to make it this way, and I've come to the conclusion that it's ultimately related to adventure design. Going from that, I'm using a challenge system that takes into account not only the power level of the party, but also (and that's really important) their resourcefulness, through a number of tags like wilderness, healing power, diplomacy, investigation and combat.
That said, I'd prefer if the various "advantages" of D&D could be tracked and developed in a way that made each class well suit for some environments, not all of them. I'm not giving support to the idea that each class should be given some time in the spotlight while the others wait, but I believe that the designers should come from the assumption that the game cannot be defined by four roles only, and not all parties need all roles to be successful. A ranger is well-suited for an adventure that uses tags such as combat, stealth and wilderness, while my preferred cleric would be tagged to succeed in situations that require healing power, combat and diplomacy, probably.
That would make for better adventure design and the end of the "need a cleric" syndrome, without necessarily killing the role of healer as a viable one in fantasy gaming.
Cheers,