It's fun to compare and contrast the games of the BBS era to mobile games today. In the BBS era there were countless time-regulated games such as LORD, Trade Wars, Usurper, and many more. By 'time regulated' I mean that you were given a certain amount of turns/energy/etc per 24 hours, and then had to wait to do more. It's literally the exact same model the seemingly vast majority of 'free' mobile games today use, except they did not try to coerce users into paying for more energy/turns/moves/...
That's on the BBS itself. E.g. a regular account might get an hour per day whereas an 'elite' might get 4 hours per day. BBS' were of course run through phone lines and while many operators set up multiple concurrent lines, access was still relatively limited so time limits on the site were necessary. Donors, by contrast, enabled operators to expand their service and buy even more lines and so on.
The games themselves are a different story. It's of course impossible to prove a negative, but I certainly never experienced any paid cheating or favoritism in Trade Wars - which I played on dozens of different sites and later on on the large telnet sites once the internet became a thing.