The difference between reacting within 6 seconds or within 24 seconds (assuming 2 successes and 2 fails) does not necessarily strike me as unrealistic. Especially in situations where a PC needs to fight her way through enemies just to get to the downed PC. That could realistically take a few rounds. But, I get it - that's not exactly what you are talking about. You're talking about the "meta" thinking of the players who believe they can stay the course for a few more rounds before the downed PC is really an issue.
In any case, delaying because a player thinks his character has plenty of time to stabilize his comrade does not come risk-free. There's always a chance of the downed PC rolling a 1, or being hit by a melee attack for two fails (if not outright death for negmax HP), or auto-failing their save against a DEX AoE spell.
All that said, if you feel it's a problem that the players are delaying their stabilizing/healing, you as DM can just make sure an enemy DOES target the downed PC - be that a goblin going for a cowardly death stab or a wolf looking to sample the menu before dragging away a meal to the pups waiting at the den. That should get the discussion amongst the players quickly going in a different direction than "oh, never mind fallen Fred just now, we have at least 3 rounds to stabilize him".