The system badges are indeed hardcoded and uneditable in the UI, though you could disable the default Nice Reply (et al) ones and recreate them as custom ones with an extra clause to exclude your user id to prevent you from earning any more.
It’s not quite the same as the feature request to suppress notifications for them, but it might be an alternative workaround.
Badges are only automatically removed if the ‘Run revocation query daily’ option is ticked on the badge setting page. If that’s unchecked then people would get to keep them even if they no longer qualified for it. (The system Nice Reply does have it checked, but you can’t edit it anyway, so this is more an FYI 
)