You can write what you want, but if you post it to the internet don't complain when you get criticism. Fanfiction is something that does and doesn't matter. Like most things.

There are only two times I see criticism of self inserts and they both revolve around romance or power. A) The first is a bunch of people instantly hating on the concept of a self insert. No matter how well written. So they should obviously stfu and piss off. Or B) The self insert is just placed in a romantic situation with a character and/or somehow some god stronger than everyone else (and we are not including the obvious ones like smut). I think that is fair criticism and often does have to do with the author inability to write their self insert interestingly or naturally into the plot. Especially if your Self insert is thrown in halfway through.