I hope I didn't get it across as an attempt to insult as that wasn't my intent. Its just looking at it from a mechanical point of view - in the sense of 'Is it worth putting time and effort in making this feature to give the players a different experience'.
From my perspective this is where the mechanic fails. I also wouldn't do it as a DM at my table in most cases - I would base it on has something changed for the character that would make him/her view the situation differently - otherwise it just becomes a numbers game with no stake beyond patience.
As mentioned you have 4 rolls + all companions in camp - making it quite a high chance of success to begin with, so why even bother making it a chance and not just giving the result to the player before putting in minor hinderence like a DC 10-15 (I guess most cases in this game are DC10) under the circumstance of re-rolling for every character after each long rest? That's a guaranteed success anyhow.
