@Mattwo7 These are some serious mental gymnastics you're resorting to to justify not including such an obvious QoL feature.
First of all, Trigger Quests as a category will always be relevant, because new ones get added almost every new Urgent, and, as such, will always have relevant rewards, even if individual quests get outdated.
Second of all, the fact that you can't even browse Trigger Quest parties in other blocks than the one you're in is a massive hindrance to forming groups. You've acknowledged yourself that Trigger Quests can be activated at any given time, so why wouldn't you want more people to see them when they are active to increase the chances of the group filling up?
And the third point, the one that OP highlighted very clearly, a Trigger Quest that wasn't started is a trigger wasted. Triggers are scarce, so it's only natural that you'd want to keep the trigger if you don't actually end up using it for its one and only, very intended purpose - actually running the quest. If, as you've said, "there'd be no guarantee other people would be doing them or if there'd be enough people in general", why not have this extra security?
This suggestion is nothing but positive, and implementing it wouldn't be that hard: consume trigger only when the quest has actually started, and add a "Browse all Trigger Quest parties" menu at a quest counter