I've always thought a hybrid system would be best.. Priority list freezes 12-24h out.. (somewhere in that range)
Anyone listed before the cutoff is in straight date of hire, can upgrade to S2
Anyone listed after cutoff is time of listing/checkin.

I've had more than a few instances of Grandma lists her and her 4 grandkids LAST MINUTE.. I'm talking under 2 hours to departure, to go to NYC to "See a show" then me (commuting) or me and my wife (vacation/other travel) are now scrambling to figure out alternates. I've seen at least 3 instances of 'grandma flying with grandkids but they are all S3s', I know there are some grandparents raising their grandkids, but being as I saw them get dropped off with mom in one of the cases I kind of call BS on it.