I can red crate each time, so I don't think I'd ever apply a conquest cron. What would it get me? Nothing more than I get right now.
I've seen a few suggestions in this thread around an omicron to make progression faster, but that would mean an ability on a character somehow having an effect outside of the battle part of the game (apart from kills/debuff/dodge type counting being double, which could be counted that way I guess). I don't see them doing anything like different stamina use or keycards or anything else that is not in-battle.
The character not being needed for feats of a future conquest would be another reason to not apply an omicron. So like someone else suggested, the cron making them count as all faction tags could help with that, but I highly doubt they would remove that particular spend incentive that these faction feats create.
I just don't see them adding anything that would make me use an omicron up this way. Not while omicron abilities are so abundant and the material is not, anyway.