I find the problem with parties with no white mage isn't that you need a white mage, it's that other classes with healing ability refuse to face the stark reality that their healing is the single most important thing they can do for a group. Any WHM who isn't a complete moron has accepted that his primary job is healing, and in fact, he has very little else that he can do. And to heal, you don't need to be the proper level, expensive spells, up to date skill levels, or even a decent MND stat, all you need is raw mana.
The only problem is that RDM tend to want to melee, BLM want to nuke, and that PLD simply can't accept that he could cut the downtime in half if he would assist healing instead of saving his TP. Now, if your party is disciplined and experienced enough, it's not a problem, but that's a pipe dream most of the time.
I, for one, am a fan of people who are willing to leave parties if they feel it isn't working. If you're a leader, the good players will stay as long as you show yourself to be competent. And if you're joining someone else's party, you're not really doing anyone a favor by staying in a ****** party. Either you're better than the ****** party and could be helping a competent party form, or you're contributing to the party sucking and they'd be better off without you anyway.
If I join a party and the party composition looks unworkable, rest assured I'm already messaging other leaders. While it's true that good players can make any party work ok, a party with perfect composition can still suck horribly with bad players. Why cripple your chances by starting on a bad foot with a badly formed group? Not to mention the fact that any leader recruiting my class instead of a class he badly needs probably isn't very good anyway.
When forming a group, the first thing I get is a mage who can heal. And if I can't get one, it's very simple: I join another group. That way you don't have to wait half an hour to fill that last spot with a healer, retention rates improve, and you're not forming extraneous groups in a zone.