Eliot Cracks the Conundrum

I want to take a moment to highlight Eliot Wilen's proposed solution to my Cleric Conundrum:

I probably don't know what I'm talking about (since I haven't played D&D in decades) but maybe a solution is just to give EVERY party a periodically-refreshed, shared pool of healing dice without any need for a character to actually administer it. Scale the pool based on the total number of levels in the party or something.

I think Mr. Wilen may be on to something here. What if healing were simply a group meta-resource? How would you determine the number of points in the healing pool? How often would the pool refresh? Who decides when to draw points from the pool and when can it be done? Does anybody have any thoughts?