The problem that I have with a system similar to frontlines is that it doesn't necessarily fix the problem, is it creates just as many problems as it solves

Firstly, it puts duties that people dont want under a microscope, or at least in sets (assuming you need to be max ilvl to queue). Will some people queue for Daily Alliance Raid just because they can, sure. But it also creates a problem where in people knowing what duties are in the pool for the day will actively avoid running it, say for example it's Crystal Tower, you dont wanna run those, so you just skip it for the day and maybe do fates or something else instead.
Secondly, the reason it works for Frontlines is because PvP is just level 30 duties. If they were to implement something like this for Alliance Raid, it creates an exclusionary problem. People who are maybe picking up SAM and RDM can't run Daily Alliance because they are 50 and the daily Alliance Raid set is Mhach or Ivalice. Also to kinda throw this out there, I am sure there are a lot of people who ONLY have ARR and HW because they were free for a limited time before 5.0 came out, locking them out of the roulette 1-2 days doesn't seem fair.
Thirdly, it also creates a problem for people unlocking duties. Sure it might help you for your queue if you happen to queue up on that day (and yes I am assuming that the duties wouldn't locked for individual queue). But say you work a schedule that only allows you a few hours a few days of the week, and you just hit 60 and wanna run Mhach, but all the days you are free to play, you can't get a queue, because Crystal Tower, Ivalice, or Nier are in the pool those days.

HOPEFULLY the moogle tomes being HW duties, will help create an incentive to run those, as I do genuinely miss running those, and might be the incentive we need to start seeing more evenly distributed duties (or The Copied Factory can be added to the roulette and everyone who is 80 get thrown into that, because I remember getting Ivalice Duties a lot when queueing alliance raid back in stormblood).
Unfortunately this is a multiangled problem that no one solution can really fix, and if SQEX is to do anything about it they are gonna have to balance out the pros with the cons, because every solution has them from what's been presented and what I've thought of.