Uller
Adventurer
So in your group, you hope that at least one person who makes their save has a lower initiative than the caster, so they can wake people up before the end of the round. That's pretty different, too.
I think I highly disapprove of not rolling for initiative if you can't act. You need to know when to make a save often enough, when to trigger certain effects, and someone can always help you out.
We declare actions before rolling initiative. You can't change your action on your turn.
You make your save at the end of the round and effects trigger at the end of the round. There is lots of weirdness RAW with characters who can't act rolling initiative. Two examples:
1) Death saves. You stablize/die faster because of good dex/init roll?
2) If you roll poorly on init and are suffering from some condition that prohibits you from acting but an ally removes that condition before your turn, you can act, but if you rolled well, you miss your turn. That's pretty different.
I'm sorry you highly disapprove but my group really enjoys it.