I've talked about this with a few other people, and as expected, opinions are mixed. Some people are horrified at the idea of never having a new class again in WoW, and other people, like myself, are relieved. I really, truly do believe that adding more classes to WoW would only create headaches for everyone, developers and players alike. I'd much rather see the required resources in design, development, and maintenance go to other aspects of the game such as dungeons, raids, scenarios, quests, and events, than to creating and continuously balancing still more classes. So, without further ado, I present three arguments as to why there should be no more new classes in WoW.
1. There are already plenty of options
Each existing class has three specs, except for druids, which have four. That is a grand total of 34 different specs available to play in the game. Not every class has wildly differing specs -- mages, for example, basically function the same way as arcane, fire, or frost. However, some specs are so different from each other that the only thing tying them together is basic flavor. A balance druid plays very differently from a guardian druid, and in many ways may as well be a different class.
Even when some classes (such as the mage) do have similar functions with all three specs, each spec must nonetheless be tuned and treated independently. Frost mages have long been considered a sub-par raid team member compared to their arcane and fire brethren. That's changed somewhat recently, but no longtime mage will quickly forget the fact that for many years frost was considered a mage's PvP spec and little else. Bottom line: there are already 34 different ways to play this game. That's quite a few. Do we really need 37?
The 34 individual specs already discussed is an enormous amount to tune and balance. We can already see how difficult the balancing act is for Blizzard developers. Each new patch, and hotfix within patches, brings changes -- often big ones -- to both specs and entire classes. Ask paladins, who have had to relearn many aspects of their class with just about every new expansion that's been released. Or death knights, whose spec directions changed utterly from their original intention between their introduction in Wrath and the release of Cataclsym.
Especially in PvP, a new class can really shake things up. Existing abilities have to be tested against the new ones being added to the game, and the new abilities have to be tested against the existing ones. The amount of necessary balancing and tweaking takes a very long time. It's a lot to adjust to for players, and a lot of work for developers. And the more tweaking and changing and refining needed, the more likely players are to become disgruntled as their play experience changes again and again and again.
3. Class development has evolved toward homogenization
I find it hard to justify the necessity of more classes considering that the ones we have have seen considerable homogenization over the course of the game. Many classes' once-unique buffs, for example, have been condensed into the same thing (see: Blessing of Kings and Mark of the Wild). To be clear: I am not unhappy that these changes have been made. Many of them were absolutely necessary for the sake of success in 10-man raiding. If Blizzard truly wants to embrace the philosophy of "bring the player, not the class," then no one class can ever be so good in terms of what it brings to the raid table to justify bringing it at all costs. No one class can ever have an ability that is both unique and necessary to the success of the raid.
I've heard some folks toss around the idea of a bard class or something along those lines; a class that focused primarily on support roles instead of active DPS or tanking or healing. The problem with a support class is that I fail to see how it could not become a necessary addition to the raid team. If a class exists that is solely, or even mostly, support, then in order to make that class worth taking to a raid, the encounters have to be tuned in to make it worth taking to raid. If it weren't necessary to take a support class, why would a raid leader choose that over a better DPS class that would get the boss down faster? And if an encounter is tuned in such a way as to make a specific support class necessary, then the whole "bring the player, not the class" mentality is out the window. This is the reason why Blessing of Kings and Mark of the Wild were changed to be the same thing -- so that your raid didn't need a druid or need a paladin.
Overall, I personally think that with regard to classes, and class balance, WoW is complex enough as it is. We don't need anything more. I would much rather see Blizzard's developer resources put into creating more diverse content than creating, and maintaining, a new class. I can only hope that Blizzard feels the same way.