Wow I think you are on to something with the sunken ship effect. I looked it up and it's called the sunk cost effect. Apparently this effect causes humans to have a hard time giving up on something even if it stops being a good thing for them because they have invested time or money or that they developed some emotional attachment to it. There was a different game called Farmville that had this similar concept of sunk cost fallacy where the players would set alarms in the middle of the night and lose sleep so that they wouldn't lose their crops.
My concern is that most people don't even realize that they have fallen for a sunk cost effect. A lot of kids play these kinds of games and I'm sure they've never even heard of the concept of sunk cost effect. Even I didn't know there was a psychological concept for what I described in my OP. So as you said, you can stop if you really wanted to but it is very real that this sunk cost effect makes it very much harder to stop.
If you don't even realize that you have fallen for a sunk cost effect trap, it makes it that much harder to quit. You don't really expect there to be this sunk cost effect in games. Usually you play and enjoy the game then it ends.
So thanks for bringing the sunk cost effect up. I think that will make it easier for people to recognize when it happens and allow for better decisions to be made. I'm glad I created this OP because I learned something.