Added*

As a mage who plays solo most of the time, the prospect of tanks and healers getting goody bags with rare mounts and such in them does kind of piss me off. I'd much rather wait in a 40-minute queue if it meant I got equal access to those goods. I get that everyone has different priorities, but it's annoying for ME since I can't exactly solo as much older content as some of the less squishy classes, too.

If you 85 gear you shouldn't have many issues. Those bc and classic dungeons are push overs.
If you're not already, you could try frost, ice barrier, no pushback icy veins, and deep freezing those bosses makes it really easy.

(not to mention strath is already a level 40-50 something instance, home of the death charger).
I have personally soloed magister's and it was easy.
No comment on anzu, never tried cause I lack the rep.

Its only equal chance for a mount in a particular run. However, a tank that is aiming for a specific mount will get more attempts in due to instant queuing than a dps is, so they already have a higher chance than dps.

In any case, chance is a fickle thing. I don't know the exact percentages for a mount to drop in these things, but if its as low as the holiday goodie bag, its still gonna take some time to get them.

I think N-Train gets to the heart of the matter.

PUGs are a crap-shoot now because that's the design. They wanted us joining guilds and doing guild activities this expansion. Guild leveling was the carrot, and dungeon difficulty that requires an almost PUG-proof level of communication and cooperation was the stick.

In a way, this Call To Arms can be seen as an admission that they can't force us to fill out a guild application after all. They're trying to make PUGs less painful, and that's commendable, but it comes only as a Plan B.

Ya, I really think it's unfair for the classes that are forced to be dps. A better way to fix the lack of tanks would be to provide an extra class with tanking.
Shaman for example were clearly intended to be tanks in the begining and the idea was scrapped. They could implement tanking on shaman and it'd help decrease the queues as well without providing a bonus to part of the players.

"I get that everyone has different priorities, but it's annoying for ME since I can't exactly solo as much older content as some of the less squishy classes, too."

A lvl 85 character of any class can solo vanilla and BC dungeons and it doesn't make a difference if you're squishy or not since your health pool is now obscenely large in proportion to the enemies and they go down in seconds anyway.

Wrath dungeons might be more challenging to solo for clothies but I don't know if that's relevant since all the mounts mentioned were from vanilla and BC.