See
http://www.pigskinrevolution.com for a tool that ought to be used, but is not. Any team that starts to use that tool will gain a significant advantage, perhaps enough to win an extra game per year. Any rational assessment would be that an extra game is worth millions of dollars to a professional team. They could choose to win more, or they could save millions of dollars in player salaries and win the same amount.
Football teams don't just blow the decisions in the endgame. A common mistake is punting on 4th down.
"Yet on the 1,100 fourth downs where Romer found it would be best to go for it, teams kicked 992 times." It's very commonly correct to go for it when it is 4th and 3, or even 4th and 4, and it can be right when it is
4th and 8 even with plenty of time left. No team goes for it on 4th down when it is marginally correct.
Decisions in other sports are not nearly as bad as the ones in football, although there are many individual decisions which are pretty bad.