A core gameplay component in the RPG's of yesteryear was the management of a limited set of resources. In particular, the number of spells that could be cast in a given dungeon were limited, and your gold was limited which meant that you only had a certain number of potions and magic items to take with you.
This meant that a large part of the gameplay revolved around the player's decisions on when to use those resources. You don't want to waste your big guns on the punier enemies that you run across, but then again you have to make sure that you can still handle them without becoming too injured, otherwise you'll have a tough time later on.
Further, healing was especially scarce. Most healing spells only healed for a pitiful amount compared to your HP, and they were touch range with a long cast time to boot. This meant that healing was relegated to post-combat usually. The focus was really on mitigating damage as much as possible in the first place, through smart use of spells and abilities - your HP pool was there as a margin for error.
Fast forward to current (online) RPG's: spells are spammed. Damage comes flying in by the thousands. Limited use items are a dime a dozen and can be farmed up the wazoo before entering a difficult area. The fundamental RPG gameplay notion of limited resource management is gone. This is why MMO combat feels so dumbed-down - all the strategical decisions have been made before the combat started (your character build, your team's build), leaving the players to just go through the motions.
Forget the fact that spam heals at range do not agree with any fantasy lore ever created whatsoever (no, WoW books don't count). The spammy spammy nature of healing is killing off one of the few interesting areas of RPG decision making, and sapping all the depth out of most games, leading to posts like this one (which inspired my mini rant here).
Design should be based instead around damage mitigation. Light healing is ok, but shouldn't completely reset the scales after each battle, otherwise to be a challenge EVERY SINGLE GROUP OF MONSTERS has to have a fair chance of killing someone in the group (leading to many current MMO 'hard difficulty' options where enemies can just 2-shot you).
Guild Wars has done some impressive work in this area with the Protection line of skills. These are used far more extensively than healing skills in PvP. Sadly in PvE people mostly resort to the good ol' trinity. There are probably a few reasons for this - a big one is that tanks already mitigate damage to a large extent, and so often the only stuff that gets through is stuff that ignores most damage mitigation. It's clear that getting rid of the spammy spammy nature of healing goes hand in hand with getting rid of the notion of a tank that can miraculously 'hold aggro' with magical taunts that also have no basis in any lore I've ever heard of. That means, of course, changing mob AI and a bunch of other goodness.
Another necessity seems probably to limit the number of limited-use items that can be used by the team during a dungeon crawl, to prevent simply stocking up on a pile of them beforehand. Alternately, such items could be made available during the dungeon crawl, rewarding adventurers with more power for exploring off the beaten path a bit (but of course with the added risk of burning more resources than you gained on fighting the extra monsters that you'd encounter... Strategical decisions, no?).
An interesting 'half way' solution is the Halo combat system. Each group of enemies there have to punch through your shield before they can damage your health. The shield regenerates quickly after each fight - your actual health, not at all. This avoids painting yourself into a corner where you simply can not possibly beat the next group of enemies, while still limiting your resources over the course of a level (aka dungeon).
Expansion of this idea would, I think, be the best way to go about overhauling MMO combat systems to be a bit more deep and a bit less auto-pilot. Also, when you have to focus on protecting people, you get to *gasp* pay attention to the actual game world, instead of watching a bunch of health bars. Everybody wins! (cue wining of people who say "omg I play healer in every MMO don't tell me how to play!!!!~1111")