I think u should be able to catch bandets. Then after you catch them they can level up ur sylesltis for 200 for each level u want ur sylesltis to go up to. And once a week they can bring u really rare items from there travles.

I believe that is generally what the folks call 'slavery' and is typically frowned upon by society in general.
Because the bandits are people. They're human people. They're jerks maybe, but they're still people. You can't keep a human person as a pet like you do a weird magic fox or a magical nature bear.

I've seen people want to be able to catch vorkids and mycanoids before, but never bandits

(that aside "level up your sylestis for 200 for each level"? I do not understand this, maybe it's just the phrasing, but I'm legitimately not sure what it means, since the level cap is 70?
I get the feeling the answer here for what you're after is perhaps "send your pets on missions"? Since that gets your pet exp and you get gold and mission satchels which can have useful stuff and the very rare chance of an essence drop?)