If I were in charge of 4e, I would just end the double-personality of HP. I would say, flat out, that HP loss is fatigue, loss of nerve, battle confusion, bad luck/'your number coming up', loss of support from your god, whatever, but NOT physical injury (physical injury would be rare for PCs and tracked separately from HP). Therefore, you don't need to 'heal' back your freshness, mental composure, fate, etc. A few minutes rest and you go back to full HP--no healing required. You catch your breath, shake off your fear, etc. and you're back to full HP (or maybe 80% if you're a realism freak).
If a character does happen to take a physical injury during a fight, then she'll need a healer, but this will normally happen after combat, or be a very dramatic event during combat, so there's no need to worry about the healer not having cool stuff to do during combat (because his healing powers are either used after the fight is over, or constitute a cool event in and of themselves during the fight).
Just my .02. And for all my wishing, I'm pretty sure it'll never happen.
In my current game we are using something like this. The spell point system from UA is used (so cure light wounds is 1 spell point) wich is almost like unlimited down time healing. But to represesnt actual wounds, when HP = 0 all further damage is Con damage this gives everyone a cushion of extra damage they can take, wich helps at low levels. Healing the Con damage follows normal rules, so you need restoration spells for it.
It has worked out amazingly well, makes everyone happy in our group atleast and everyone understands that hit points do not equal taking a stab in the gut or an arrow in the shoulder that is what happens when you start to lose Con.