Auto-queue for M+ won't solve your problems
Since M+ started, the "I can't get picked to a +2 groups even tough I'm a a dps with a billion ilvl e a trillion rating" post also started. Most dps seems to think some sort of autoqueue like heroic dungeon would fix it.
But it won't. The reason people aren't getting invites as dps is simple: the PL choose a dps with better gear/rating/group utility. Which is not hard to find when you consider the number of dps in game.
As a healer, when listing my key I always take the first tank and choose the dps accordingly to what I think the group will need. Party buffs, brez, lust...
The real issue is - the tank/healer:dps ratio is broken. Even with autoqueue it'd take forever to find a party as dps. Not to mention, majority tanks and healers would probably still prefer to form their own groups.
I think the best way to solve this issue is making tanking/healing more attractive to players.
(Also, it's still the first week, if you really want to push and get all achievements or something so soon, you need a pre made group).
(This is not to hate on dps, I play dps on my alts, i have dps friends)
(Healing doesn't seem to be in a bad spot per say, considering I'm playing a "non-meta spec")