The problem with having a melee healer is that there can be multiple targets up at any time, and it can be hard to track down which player has taken damage and where they are in relation to you. I've had some experience playing a DPS class. In fights where there are multiple mobs involved, I might periodically lose track of which mob should be taken down first. Healers don't exactly have that much of a luxury because there's no time to keep moving marks around to designate healers. It isn't practical have nameplates and go from person to person as needed to heal them back out of lethal damage range.
There is only one class in the game right now with two talent trees solely dedicated to healing. Priests are fortunate in that regard. Players who are interested in healing as a priest get their choice of two specs, which can both be used effectively to keep the other players alive.
Looking at the different models, we can make a few observations about how they would play out for healing classes. Before we proceed with the discussion, let's make the assumption that it is entirely possible for multiple healing specs within a class.
Model 1: Equality For the most part, this is the model that's currently in the game. Across the different healing classes, you could bring in any combination of healers and specs and accomplish the goals. Certain raid encounters and bosses might promote the strength of one class over the other, but they're all expected to stay within a reasonable performance level relative to other healing classes.
Model 2: Specialists Different healing specs would be catered to a really specific job in a fight. Powerful AoE healing gets one spec, while single-target healing belongs in another. Before the priest class became what it is today, it was often stated that discipline was the go-to spec for tank healing and holy for AoE healing. That distinction is still apparent in some circles. But imagine if shaman had Healing Rain and Chain Heal restricted to another spec or if Earth Shield could only be used in the one meant to single-target healing. Our healing compositions would be different. There would be an extra layer of organization and recruiting that had to be done. Guilds wouldn't just be looking for healers or paladins. They'd be looking for divine-specced paladins (or something) who could heal more than one target way more effectively than their holy-specced counterparts.
Model 3: Utility I'm not quite sure how much more utility healers can get between all the raid-saving and mana return cooldowns that are at the disposal of players. Having a healing class that buffs other healing classes doesn't seem popular. They wouldn't be seen as important since if their sole presence there is to provide utility and buff everyone else, their direct contribution to the players around them wouldn't be apparent on the meters (which, like it or not, is a metric for performance).
As an aside, I remember that one raid incident when multiple shadow priests were brought in back during classic Naxxramas, leading to a progression kill.
Model 4: PvP vs. PvE You'd still have multiple healing specs, but the different skills and strengths would correspond to whatever activities you were doing at the time. Each healing class would then have a spec meant for PvP and one meant for PvE (with some overlap). Again, using priests as an example, discipline is often renowned for PvP players. But discipline and holy are equally viable in PvE.
Model 5: Removing roles from the equation Tanking shaman and tank priests! Every class inherently turns into a hybrid and has the tools to do anything that the game calls for.
On the one hand, a part of me would be curious as to what the game would be like today if the Model 2 style of roles were implemented. But then another part of me recognizes that if a crucial healer died, there might not be another player who can cover for their job (assuming there was no way to bring players back to life). I find it illuminating when reading about the various insights into gameplay and class designs because then you get the opportunity to think about what you would do if you were in their position. It would be like watching sports and yelling at the TV for what coaches should be doing. In gaming, one could call it armchair developing.
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