Heroes that chose themselves

Hello op, may I introduce you to Harry Dresden?

I like this. Fuck fate and destiny, there's only one way to make sure a job is done right.

Less Po's more Tigress'

Bruh half of the heroes are like that

This is why I like Wind Waker so much

Does Megamind count?

Even in the fantasy genre, where most of those types of stories are, there are plenty of stories that don't follow that particular set up.
Sounds more like you watching/reading the wrong stories more than something that's actually missing in stories.