I'd like to have a rule across all 4 major North American Sports (baseball has it right).
In Football and basketball, if the score is tied at the end of regulation; play a fifth quarter. If it is tied in Hockey, play a fourth period.
If it ends in a tie after the end of the quarter/period, then maybe have some augmented way of deciding who wins. The OT rules are silly and the reason for them is sillier still. In 2002, there were 25 overtime games in the NFL. That is the record for a single season according to CBS Sports.
The NFL has seen an influx of overtime and ties this season
www.cbssports.com
That means that there were less than 2 a week. Some teams may have played none. Football (unlike Basketball and Hockey) has offensive and defensive specialists so a specific player will not be on the field at all times during that arduous 15 minute fifth quarter.