I suspect that the reason why this won't happen is much more practical than what we are discussing.

The story modes for those primals are 4 man fights; while the trials are all 8 man. There would probably be changes required to the code to create exception cases if the change were to be made, which isn't great. (This also explains why Praetorium and Castrum have their own queue. They are really levelling dungeons at this point; but they are the only 8 man ones we have so far.)

Add to that player expectation when queuing for a Trial roulette. When I queue for one, I'm expecting a 5-10 minute fight. While that might be fine for Ifrit; Garuda storymode is objectively more difficult than Hard mode. The iLvl for hard mode is such that people don't even bother with most of her mechanics. The level sync on storymode, however, makes it so that failing her mechanics will still wipe you.

What I'm trying to say is that if I queue for Levelling Roulette; I've planned to have 30-40 minutes available to see it to its end. So if Garuda goes poorly, I'm more likely to stay than if I had planned a 5-10 minute thing at the end of my night. I suspect this was part of the reason why people would drop out of Steps of Faith (even post-nerf, if I remember correctly) or even Chrysalis.

For the producer, you're going to want to balance risk and business value when deciding what your team works on. This feature would seem like fairly high risk and, based on most of the feedback in this thread so far; low business value. I, personally, wouldn't prioritize it either if I were them.