Originally Posted by
Rimurutheslime
You can look at it like this, Private servers are different entities compared to the main game. They share similar traits, animations, heck you could say it's a carbon copy of the game but essentially they are different in some sense as you need to create a new account.
To summarize: It's like having facebook and twitter, both are similar social media platform but you need different accounts. And no you wouldn't get banned as you are going to create a new account, not transferring your main acc.
The purpose of private server are for those people in the past who were having a hard time farming as farming items in private server are far more easier.
I hope this answers your question.