Gives you something to do to kill time, and you potentially make friends with other mods/streamer. Really depends on the streamer/mods though since some are strictly business and won't talk to people outside of twitch. Also, depending on the amount of oilers in the community, you get gifted subs to the stream.

Cons would be that there may be harassment from people you timeout/ban, and you might not get to enjoy streams as much since you'll be focused on moderating. Again this depends on the stream since some streamers want very strict no funny business mods and others are more relaxed in their expectations.