Yoshida and team deliberately excluded Coil from the Duty Finder because they wanted end game to cater to 8 man setups and for those who roll deeper than that they have in store Crystal Tower which is 24 man raid content. Once Crystal Tower is implemented they also intend to update both Coil and Tower in a alternating fashion. If I recall correctly from Yoshida's Game Watch interview he basically lays out that as content gets harder and harder he wishes for players to realize that they'll need to form groups if they want to see any progress beyond the HM Primal Fights. He even says how this should become apparent to players by the time they reach Titan HM if not earlier, essentially that the higher up the content ladder you go the more the grouping training wheels come off and it's up to you to find or start a static-esque group.
I suppose the above is neither here nor there though as the OP is concerned about people who are inevitably cut from Coil runs, assuming you will roll with 24 people anyway to do Crystal Tower runs. Or catching up friends who are missing a specific turn win. In the latter case though I thought you entered a Turn based on your Party Leader's progress couldn't you simply make party lead the person in question that you want caught up? I'm nowhere near the point to do endgame at present so forgive me if my last point was addressed.