See, here's the thing. Nobody's actually stopping anyone from trying to make money from forum games. No, calling someone foolish for suggesting it isn't stopping them.
In fact, it occurred to me that people have made money from forum games. MSPA started as an ISG. The ones before Problem Sleuth happened on a forum, iirc, and Problem Sleuth was essentially run as one. Even the very beginnings (and some intermissions) of Homestuck were, and it always maintained the veneer (with the >_ at the bottom of every page). Andrew Hussie made a living out of it. So if you have a large enough audience, you too could start your own website, put up ads, sell merch, and not know how to satisfactorily end your magnum opus.
I wouldn't want to, though. Being paid for your hobby might sound nice on the surface, but a job's a job. And a freelance job is a big risk.
For example, my sister is a photographer. She loves photography (and puts a lot more work & skill into it than I put into forum games). She deserves to get paid for it, and she does. Usually. But sometimes she gets a call; "Oh hey, we want you to work for twice as many hours, but we can't increase the budget. But you'll be working with [celebrity], so think of the exposure!". She did the math; after the cost of equipment, she'd be working for less than minimum wage. So now she can either accept this terrible offer (and be miserable doing her hobby), or reject it (and earn nothing, because she probably can't find another job that quickly).
The same risks would apply to a professional forum-gamer. "Oh hey, you didn't get as many views this month, and now you can't pay rent." "Oh hey, people didn't like the latest update so a bunch cancelled their patreon subscriptions, so now you can either cave to financial pressure and change your art, or fail to pay rent."
Note that even if it isn't your main source of income, the same issues can apply on a smaller scale. Having a donate link that earns you a few bucks every now and again is fine and all, but I wouldn't want the pressure it would create- "I got a bunch of donations for this update... I have to make sure the next one is as good, otherwise I'm ripping off those folks that donated" "Nobody has donated to me in months... I guess that means I'm not making good stuff any more".
Also, it could create pressure for viewers; "I really liked this update... now I feel like I have to donate"