The problem with class specific tags isn't a contention of whether or not they are useful - the problem is one of consistency: how the tags are used are just as important as whether they're used at all.
Tags exist as means to filter and identify questions!
We've got a fair number of questions on how to respec your character. All three of these questions have ambiguous titles that could apply to any number of games. Yet each of these questions refers to a specific game. Users cannot judge their ability to answer the question based on the title alone, so they use the question blurb and the tags to decide whether or not to open the question.
This is part of why we don't require game names in the title - it's in the tags, and that's good enough when it comes to identifying the requirements of a particular question.
Tags exist to add information about a question!
A while ago, we had a dwarf-fortress-fun tag. In Dwarf Fortress, "Fun" is related to losing when things go catastrophically wrong - but that's only because it's a bit of an in-joke within the Dwarf Fortress community. But you'll notice something: The dwarf-fortress-fun tag has been removed from Gaming. It added zero information (all dwarf-fortress-fun questions are dwarf-fortress questions), and on top of that, was used inconsistently - either you knew about the joke and added it when things were going catastrophically wrong, or you didn't because you didn't.
The [Dwarf-Fortress-fun] tag was not fulfilling its role as a tag, so there was no reason to keep it around as a tag.
Which brings us to the crux of the argument:
Game-Specific Tags are hard to use consistently
There's two separate issues here that make consistent use of the tag hard. First, there is a sort of "Double-Standard Ignorance" going on: most games have only one tag, so the less savvy users will stop at one tag, especially if they have a clear idea of what they're asking and don't need (or bother to use) the tag auto-complete.
How many minecraft questions have we retagged [minecraft-redstone] because users were unaware the latter existed? (Perhaps Agent86 could whip up a script to tell us!)
Then there is the separate issue of "Content Threshold". How much redstone needs to be in a question for it to be minecraft-redstone? Is it a minecraft-redstone question if they want to open a door with a pressure plate? You could use Redstone, but you could just as easily put the pressure plate next to the door, avoiding the issue entirely.
Soldiers are the only class capable of using The Black Box - should questions asking about it have the tf2-soldier? What about a question asking how much damage fire does? Sure, tf2-pyros are the primary way to set someone aflame, but tf2-soldiers, tf2-snipers, tf2-scouts, and [tf2-engineer]s (I think?) can all use fire - do you tag with the most pertinent classes? As many as you can? None of them?
Game-specific tags are already being used inconsistently
This isn't an issue specific to Mass Effect 3 or Diablo 3 - we've already got issues where game-specific tags are being used mostly randomly. And if the tags are being used randomly, they're not doing a proper job of filtering things.
Team Fortress 2 has a bunch of questions that fall into this problem.
None of the TF2 game specific tags have tag wikis, either, which certainly doesn't help!
But that's Team Fortress. What about the poster-child of game-specific tags, Starcraft 2?
Well, first some numbers (all of these as per the date of this post).
Total Starcraft 2 Questions: 945
- Questions Tagged Terran: 65
- Questions Tagged Zerg: 77
- Questions Tagged Protoss: 62
Even if you add all these together (and ignore the fact that some questions are tagged with both), you only get 204 questions, which, considering that every game of Starcraft 2 involves at least one of these races, seems rather low. Do we really have 500+ questions that are race-agnostic?
And again, we have Threshold and Ignorance to consider.
Why do questions like these not have race tags?
And, more relevantly, if a question mentions a witch doctor-exclusive skill, does it also need the diablo-3-witchdoctor tag? After all, there's no potential confusion about which class you're talking about. If the tag doesn't reduce confusion, it is nothing more than needless clutter (much like adding steam to every Skyrim question with pc). And finally, if it's just clutter, why have the tag at all?
Ultimately, I think it comes down to the fact that:
Game-Specific tags are not conducive to our current tagging schema.
It is a good theoretical idea, but Gaming hasn't been able to satisfactorily implement such things in the past, and there is nothing different about the situation this time that leads me to think anything differently will happen.
On the whole, I think Game-Specific tags as specific as this do more harm than good, and should not be used for individual character classes.