I think that people gamifying gamification systems is always going to be a thing, because… people.
I have pretty strong feelings about badges. They’re powerful motivators if they’re for reasonably robust goals but I think that if you have lots of them and they are easy to get then they have little to no worth most of the time. They just end up creating the kind of mess that you’re experiencing, and add little to no value for everyone else. They certainly don’t encourage healthy long term behaviour change.
It’s not actually even about the number of badges. Lots of badges that are very hard to get but signify something important are powerful.
I’d definitely consider disabling badges and redesigning your gamification system to encourage the kinds of behaviour you do want to see.