I don’t know what the process is like to become a certificate authority. I imagine the answer is technically yes but realistically no, at least not as an individual. You’d be providing a critical piece of internet infrastructure, so you’d need the world to consider you capable of providing the service reliably while also capable of securing the keys used to sign certificates so they can’t be forged. It’s a big responsibility that involves putting a LOT of trust in the authority, so I don’t think it’s taken very lightly.

It’s to make sure you’re actually reaching your intended endpoint. If I’m visiting a site for the first time, how do I know I actually have THEIR certificate? If it’s self generated, anybody could sign a certificate claiming to be anybody else. The current system is to use authority figures who validate certificates are owned by the site you’re trying to visit. This means you have a secure connection AND know you’re interacting with the correct site.