More stamina = better performance = higher point differential = more rest for starters (blowouts etc).
The high minutes depend on a lot of things, and while I agree high stamina leads to players being able to play more minutes effectively, I think it's still important to train it if there's multiple players below 5 on your team. Unless you're in a league where every game is a tight game you're not sure to win or lose, you always have opportunity to rest players if they make too many minutes in a game. Furthermore, if you have a balanced team, it shouldn't make a whole lot of difference who starts.
Let's say you have three pretty much identical players for the PF/C position, each with 8 stamina, and you're in a league that doesn't present frequent opportunities for blowouts. One of those three is going to be playing 80 minutes, barring injury or foulouts. And if you run slow offenses, you may well run above 80 minutes - I routinely saw a pair of my starting guards with 7 stamina get as high as 45 minutes in Princeton some time ago.
I do agree that generally stamina is nice. If I could make it so stamina training raised players below 5 toward 5, and pushed players above 5 down to 5, I'd probably do it much more frequently.