Public relations double-speak wants us to believe that Warcraft is an ever-evolving medium that has made leaps and bounds since its creation, but are Priests becoming obsolete? Priests have evolved quite a bit along with the game. From the beginnings as the clear best healer in the game, to the queer balance of Burning Crusade, to the Circle spamming early Wrath days, a lot has changed. Priests are no longer the jack-of-all-trades master of everything under the sun when it comes to healing, but they are now better at certain tasks than they were in the past. The truth is that Priests have fallen behind in their primary role and are being kept aloft by under-tuned content and clever use of utility abilities.
Let's begin in Vanilla. This was the peak of Priests. They were fantastic tank healers, could cover on raid very well, brought substantial utility and could be told to do anything and do it as well as anyone else. Healing consisted of Renew raid healing, with some minor Flash Heal use, but heavy use of various Greater Heal ranks. This was to deal with slow and extremely spiky tank damage that necessitated stop-casting and trying to stay out of the five-second mana regen rule for as long as possible. Priests were also helped along because Druids were incomplete and somewhat slow healers, while Paladin and Shaman were faction specific and neither filled a complete role. Priests on Horde side tended to tank heal more, while Priests on Alliance side tended to raid heal more. This didn't matter because they have strong tools to deal with either.
Then comes the 2.0 changes and Burning Crusade. Paladin and Shaman are rebalanced to be non-faction specific. Druids are given a large arsenal of heal over time abilities and fleshed out. Priests in the meantime keep their old role, but are given an extremely strong pair of tools with Circle of Healing and Prayer of Mending. Damage in Burning Crusade begins to favor a mix of heals, with Priests handling most of the large spikes and Paladins, or Druids leveling them off with a constant stream of small heals. This lead to the first Priest split between your Divine Spirit Priest and your Circle Priests. Your Divine Spirit Priest would be a tank healer optimally and serve much as they did in Vanilla to great effect. Your Circle Priests on the other hand become the dominant raid healers. Towards the end of Burning Crusade it became apparent that with enough power behind them the Druid and Paladin style of tank healing fully replaced the need for the spikes from Priests. The game was moving more and more towards favoring very fast heals that could be sustained.
Now comes 3.0, which changes everything for a second time. Divine Spirit has become baseline, but a new rift is created between Discipline and Holy. At first this has little impact, your tank healing Priests convert to Discipline and switch to the new Flash Heal healing and can now happily compete with Paladin's Flash of Light. Holy Priests find themselves stuck raid healing with no real option to tank heal when Paladin, Druid and now Discipline are all beating them easily. Now Wrath is released. More talent points are available and Holy catches up, but aided by Circle of Healing is an obvious pick for raid healer. Druids are given a new variant of Flash of Light, while Paladin's Holy Light is now able to be cast nearly as fast as their old Flash of Light. Shaman are given new tools as well and continue to fill gaps in healing. Early on Discipline is a serious contender for best tank healer with strong shields and Penance filling the old Greater Heal spike coverage.
This lasts throughout Naxxramas, but people begin to realize that new raid content pales in difficulty to older content. When Ulduar is released and hard-modes introduced they find Discipline has a new role in preventing huge spikes of damage that would be not be possible to heal. Holy on the other hand has had Circle moved back to a cooldown and is now faced with massive raid wide damage. Holy begins moving to the 'Renew spec' to better handle this after realizing that Druids were completely dominating them on healing meters. With the shift Holy catches up, but by now it's apparent that being competitive on healing with the other classes now requires a great deal of concentration and foreknowledge of fights. Discipline is now finding that they struggle to compete with Paladins on tanks as they take more and more damage exposing that Paladins healing in Naxxramas was held back almost entirely by incoming damage. Once incoming damage increased Discipline seemed to fall behind.
Then came the straw horse. Discipline began to use in game mods and parsed logs to show they're worthwhile by using shields and now argue that their absorbs should be considered as part of their healing. This creates numerous problems and while it is very useful on hard-modes in Ulduar, it gives many Priests the wrong impression about how to play their Priest and what spec they should be using. Holy began to be singled out as nothing but a cloth-wearing Druid who was a heal-over-time spamming raid healing robot. Discipline was now the favored spec.
Not long after that the Coliseum opens. Discipline rides high on its (straw) horse, while Holy finds itself with a fight it does very well on with the Twin Valk'yrs. Druids continue to pull ahead on functional healing as damage increases and Paladins continue to outpace the other healers on tanks with no stopping in sight. This is the second wave of Priests realizing that they could top meters early on mostly because they were designed to react half a step faster than the other classes. While they had been mocking the other healers in Naxxramas for fifty, sixty, seventy-five percent over-healing they had failed to realize that the over-healing was not the product of poor play, but a disparity between input and output. A tank that is hit for four-thousand can only take four-thousand effective healing. Whoever can react faster will come out on top of healing.
When four became thirty the gap became very apparent. At this point it's too late for Priests on tanks. They were moved to a Flash of Light replacement, but not given a tool to compete with Holy Light when damage increased. Discipline as full time tank healers died. Holy at the same time was dealing with the reality that Renew was weaker than Rejuvenation and their regen was not as solid as Druids. Everything they could do the Druids could trump, with a few exceptions.
Now Icecrown Citadel is released. Damage is lowered, but the consistency of that damage is increased. This favors the faster healing style, but the damage of the fourth tier of content is now beyond the scope of Flash Heal. It's too late for Discipline to make a resurgence, so they attempt to keep riding their shield spamming bandwagon, but realize more and more that people now understand them. The horse burns away and Discipline now has to prove their worth again. They're saved first by bugs on Saurfang, then a few fights that favor raid shielding for part of the encounter. Until Lich King this barely saved him, but with his encounter being known Discipline is now safe and will have a spot in raids until Cataclysm. If only for one fight.
The other impact of this new damage model is the massive introduction of damage auras, and other light raid wide damage meant to stress healers. The real impact is that since the raid damage comes at a slow rate it favors Druids more and more as gear improves. At this point another divide begins to form. Some Priests are moving to using Flash Heal as a raid heal. The hope here is to differentiate from Druids and win a raid spot in this manner. The truth is that while mimicking Druids was the original reason for the switch to a Renew-centric spec, the true purpose was because it was a more competitive raid healing spec. The passing resemblance is inconsequential if it is also the optimal play-style.
Other Priests have realized that they can provide things that Druids can't and while their healing may be behind the damage in Icecrown and (H) Icecrown is not high enough to make Holy obsolete. If it were twenty percent higher then there would be a serious issue as the gap between Druids and Holy Priests would be too large. This is most likely lucky on Blizzards behalf as they planned three tiers of content, instead of the four they eventually produced. By making the final tier a small step up from the previous, while keeping the gear increase even they allowed weaker classes to be competitive. Essentially creating a throwback to (25) Naxxramas where the difference between input and output allows Holy to keep up. Essentially if a class is strong enough to keep people alive, they are a functional healer. It doesn't matter that Druids are better if the amount they are better is primarily concealed by over-healing. The realization is still there though. Holy can bring a tank cool-down, a large pre-cast AOE heal, a speed increase, a group mana restore and a preloaded reactive heal. Now we're back to Burning Crusade. Priests fill roles not because they are better, but because they are easier to add to parties without hurting the composition. They bring utility, rather than power.
The schism is there though. Some Priests feel they need to compete on pure healing, or don't understand the utility they should provide. Some still cling to the past and try to ride old strategies to success. Some refuse to play similar to another healer, while forgetting that the other healer was based on Priests original play-style. You must keep in mind that evolution is only partially natural. The other part of the equation is how individuals react to their environment. The push towards Flash Heal Holy is missing the point and hurting the perception of Holy. The reluctance of some to adapt to the changes and learn to use the utility they can provide is leading people to wonder what the purpose of Holy is in Warcraft. The role of Priests and the power of Priests has changed over the years, but it is the inability of the users to adapt that is ultimately causing the class to drift towards obsolescence.
TL;DR: No. Go get a cup of joe and your glasses and read, monkey!
Edit: Slight edit for clarity on two points.