I understand there are some practical implementation questions involved with this, but i do believe they can be solved.
I logged on today to soak in some Heavensward content in anticipation of Stormblood. I decided to do Void Ark and Weeping City as a healer. Wait time for Void Ark was 30 minutes and Weeping City about 20 minutes. After a food break, i got together with a fellow healer from my FC and we used duty finder to do Alexander 2 and 3 normal. Part 2 we waited for 45 minutes to pop. Part 3 we waited for 35 minutes until i just got too tired and went back to playing Persona 5.
This all reminded me that a couple months ago i tried going in on the first part of Crystal Tower (as healer) and waited for an hour without success. I only ever completed Binding Coil because i used Party Finder.
Now... Party Finder works great. I've had great experiences with it. I don't mean to qualify that as to the quality of groups created, but simply that groups can easily be created with it. It is certainly an answer.
Still, the Duty Finder is badly broken with regards to these contents in particular. Sure, long wait times are natural as more and more content enters the game and time passes, but there is the system of roulette to help spread players around and fill in groups across all of that content, cutting wait times.... with the exception of Coil/Alexander and the 24 person content.
Sure, there are practical questions. I don't think it necessarily matters how many people would bother doing a Coil Roulette each day so much as just having one could help a little... Is it synced or unsynced? Naturally people will 'DC' if they pop into turn 9 like they do with Aurum Vale. How to work around this etc etc. Is the reward tomes? Maybe it is better served rewarding some kind of crafting mats or Relic mats. People go into Crystal Tower for mats ... surely they'd Roulette to get their 1+1 item each day towards whatever goal.
Anyway, sure, thanks to Wondrous Tails and stuff, there's always coil parties in Party Finder, but all this content seems just more lost to finding groups as compared to regular dungeons or primals. With Stormblood, the whole Alexander will be a ghost town too, as will the Heavensward 24 mans. Comparatively speaking. I'd love to see more solutions to this. Coil is still some of the absolute best content in this game.