A 90% chance is worse than a 99% chance. The possibility that you get nothing is not an argument to ignore the context.
Consider Russian roulette. Are you seriously going to argue that the number of bullets in the gun doesn’t matter if you only play one time?
Ah but I’m not ignoring the context. I’m expanding the context beyond “fun math puzzle” to “wow this is a game not worth playing because there’s no edge”.
Again, only applies to the non-iterated version. If you find an analog of monty hall that gives you many at-bats, play away.
"wow this is a game not worth playing because there’s no edge"
The prize is a brand new car.
The optimal strategy gives you a 2/3 chance of winning.
Over the course of your life, if whenever you have a choice to make you choose the lower probability strategy (here with the Monty Hall example it's not even an expected-value vs. variance tradeoff, switching is just all-around more optimal) you will most definitely end up worse off in the end.