Is it sometimes considered politer or more formal to say ちゃう・じゃう as opposed to してしまう？ Does it give a more positive nuance than してしまう？
An example: One time I was going to be late to a dinner date and someone called me asking how late I would be. They were nervous and I'm their senior so they were using keigo the whole time, and then I said something like "it's ok if you start without me," and they replied 「それでは、はじまっちゃいます」 which I took to mean "ok, we're going to go ahead and start then."
I mean its not a big deal to me but I was just curious because intuitively it does feel like saying 「それでは、はじまってしまいます」would be completely wrong. Something about てしまう gives me more of a nuance of agency where ちゃう and じゃう don't.