All queues numbers visible to a player are already role-specific. If I queue for a trial, healer RQ #1-2 are first party, 3 and 4 the second, etc., etc.
If I pause at position #3, #1 and #2 go in, #4 and #4 become the new #1 and #2, and I'm left waiting for a further party, just as I would have been before pausing.
If I'm healer #3 for a raid and pause, 1, 2, 4, 5, 6, and 7 enter; I remain at queue position 3. I will still join the next raid to pop from the time I unpause (or maximum pause duration expires, etc.). Depending on bottle-necks among other roles, that may be a good 15 minutes later than had I remained at my seat until it popped and I could enter, but if returning to my desk within 45 seconds were possible, I wouldn't have hit pause and taken that risk over the chance of losing my queue entirely. I have substituted a risk of being pushed back to position #21 or so, the true end of the line, with the risk of the queue popping (while I'm unable to respond) to it, thus skipping an entry I could (not) have otherwise taken.
Bottlenecks within a particular role can push the others to maximum effective queue positions well beyond just the next-next entry. I would guess that if we only ever had nearly ideal proportions (i.e. only a run's worth of the least relatively populous role short of the most populous role's runs'-worth of players) queuing for a duty, you would be right, since the difference between position # (In for next entry) and # (In for the entry after next) would be the difference between the front of the line and the end of the line. But that's often not the case, so I'm not sure it's quite so clear-cut.
That said, it may indeed not be worth the trouble to code for a doubly niche benefit. That's largely why my original question was phrased as such, to discuss whether it'd first even be feasible, secondly--worthwhile, and only finally--attractive.
NOTE: I may still be misunderstanding what you've said here. Or, more particularly, I'm not sure I believe that, say, a solo-queued individual player is bound automatically to a particular party until the time that there are sufficient numbers of each role for a party to be matched, as that goes against what I've heard from people who've analyzed this in the past. Any further links or data would be appreciated.



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