"Our goal has been to remove cleric healing as a necessary element of adventuring."
And that, IMO, is the first mistake. The goal should have been to remove any kind of healing as a necessary element of adventuring.
Whatever the game assumes to be the "standard adventuring day" should be determined on the basis that each PC has no healing capability. Healing in the form of magic items would thus enable the PCs to artificially extend the "adventuring day", whereas healing in the form of class abilities (such as healing spells) would effectively be neutral since they are obtained at the opportunity cost of other class abilities (i.e. instead of casting a healing spell, a cleric could have used an offensive spell that ended a fight early, before more hit points were lost, or used a defensive spell that prevented the loss of hit points in the first place. Alternatively, instead of playing a cleric, the player could have run another character with better offensive or defensive capabilities*).
Giving the PCs some ability to restore their own hit points (presumably, non-magically) would thus be a dial which would increase the length of the adventuring day across the board.
* In 4e-speak, you can replace a leader with a striker and the game still works because the striker will end the fight faster, thereby reducing the PCs' overall hit point loss. You can also replace a leader with a defender, and the game still works because the defender will reduce the opponents' ability to deal damage to the party as a whole. Presumably, there is a similar argument for replacing a leader with a controller, but it probably isn't as clear-cut.
