> What do these political police stand to gain from all of this?

A warm fuzzy feeling of seemingly contributing to the Forces of Good and fighting the Forces of Evil. Some launch rockets to the Moon, some create beautiful art, some create awesome software. Some instead bully people to not use certain words. The consider it their contribution to the society. Unfortunately, as more and more people fold to their pressure, this serves as confirmation that this contribution is worthwhile and there's more to come. If you write a symphony and it is applauded, you want to write another one. If you speech-police one project and it works, you want to speech-police another one.