In my experience, this wouldn't actually help what you have presented as the "problem" here.

First of all, not all hunts are "landmined" or pop right in front of the player attempting to spawn. For most you have to perform the trigger and then go look for the hunt. Just finding the hunt would eat up a chunk of your proposed timer.

Second, from what I've gathered, there are generally small groups of players that actually work on spawning S Ranks on each server. It's not generally a community effort to spawn. On my server, the S Rank spawn groups typically do an "inner circle" call first to ensure that other S Rank spawners who might be working on a different hunt mark have ample time to arrive, and then a mass call is done server wide through various hunt shells. So by the time the actual mass call goes out... it's possible this five minute timer is already gone.

Finally, because of the nature of linkshells having a member cap, relays often get staggered through various shells. Just because one player has seen a call in their shell for the first time doesn't mean that the original call didn't go out 4 min ago. I believe this is why many hunts get perceived as "early pulls" when in actuality players just got a late calls in their hunt shells.