Maybe I and my friends are overly competitive at board games, but not tying to win was not a problem for us.

Though poker and similar games were only tiny part of our games.

(except some cases where player was utterly doomed and checked out)

It's not about players not wanting to win, it's about wildly heterogeneous perspectives of winning. If we're not playing for cash, walking away in first place with $30 of the $100 bucks on the table isn't much different than walking away in first place with $80 of the $100 bucks. On the other hand, a second place win with $40 might be considered worse than a first place win with $30 dollars. With cash, those dollar amounts mean something intrinsically.

It leads to overly aggressive, low-information gameplay, because players will opt to "either win or lose by a lot" over "lose by a little".