I am new to the game, so here is a perspective of someone who hasn't played enough baseball to really fricking care, but also hasn't been around long enough to form the opinion that baseball is dumb.
I primarily got involved in baseball (in what little way I am involved), because as a new player really buying into this game I was itching to do something between turns. Now, for me, the money wasn't why I was doing it... But it really doesn't seem fair to the people that have invested in it, the dude that invests an hour or two on games isn't going anywhere near the game breaking marks you are referencing. If you nerf it per game, you are probably going to kill it for the majority of people and suddenly it is just becomes an abandoned feature.
Cap the games per day. Games per hour. Games per turn. However you want to do it or need to do it. It isn't the primary reason anyone plays the game, but obviously the feedback is telling you that it's a huge deal to a the core players that love the feature as is. You can have your cake and eat it too. Nerfing the quantity of games allowed as opposed to the quality of money per game would allow you to fix what you deem is a gamebreaking oversight, while allowing your users to continue doing their thing in a limited capacity.
tl;dr hey bruh just fricking limit the games
edit: tried to change fricking to the real word, but uh... No dice lmao