He pulled them out of his arse, which is exactly how freelance/consulting pricing works.

Yup!

That's how I started billing clients initially; basically making stuff up, estimating project complexity v. time-to-implement, and so on.

Eventually they were reasonably accurate, then I stopped doing it for awhile. I've toyed with the idea of getting back into it again, but I'm a terrible hustler, and don't have the patience for it :(

How do you find clients/work? Were you contracting?

I've always been curious about how freelancers make such a high hourly, because freelance websites are full of people charging $15/hr.

By delivering quality and focusing on clients that don't care about pinching pennies.

But do many of those clients exist on sites like upwork?

To find clients that will pay good rates you're mostly going to have to deal with them directly, which rules out most sites that try to act as a middle-man.