It prett much comes down to this:
A diploma (formal education) is the quickest and most reliable way to prove to someone from whom you want money (salary, fee, etc) that you are qualified to do the job. Maybe you can do it without the benefit of a formal education, but people aren't just gonna take your word for it, nor would you if you were in their position. The higher up you go, the more there is at stake, the better, more reliable proof you need to provide.
If I'm choosing surgeons, I'll consider all sorts of things but primarily, where their formal education and training came from and what their reputation for excellence among their peers and patients is. If I'm looking for auto-mechanics, I'll be, basing my choice solely on their reputation and references.
Everything else is a matter of opinion.