If healing is taken as a significant aspect of the game (as it has traditionally been), then non-magical healing should (IMO) exist.
A DM who decides that he's running a non-magical campaign (perhaps where the quest is to discover what happened to the magic, or even to restore it) shouldn't have to fight the system. He shouldn't have to bodge together workarounds for the fact that healing is required for a group to function as an effective party but only magical healing exists in the game (which was an issue that cropped up for me more than once prior to 4e).
On the other hand, if the designers find the "magic number" for healing, then there's a bit more leeway. In that instance, having a second rogue is just as good as an extra cleric, because the extra damage balances out the lack of healing. Having a healer in the party becomes an issue of play style, rather than necessity.
However, even in this case I think non-magical healing should exist (it's just less of a necessity). Some people enjoy playing the leader. Having a non-magical healer allows those players to play their preferred role even in a campaign where magical healing doesn't exist (perhaps because, as in early Dragonlance, the gods are absent).
I do think that for the sake of those who dislike non-magical healing, those rules are best confined within a bounded subset. That way someone who doesn't care for nMH can simply say "The Warlord class isn't available for this game" or even "You can be a Warlord but their nMH powers don't exist in this campaign", because those are the only places those rules exist.