[improbable22]

Well, that's how this was discovered, as a clever hack that worked. In the 1940s.

But it was subsequently understood much better, in the 70s. There are no infinities involved in thinking about renormalisation group flow.

That progress seems like exactly the story the article is trying to tell.

It's indeed not so different from the story of calculus. You don't even need Dirac, the very basic idea of calculus is a hack for dividing zero by zero without getting confused, which later got nicely cleaned up to became respectable mathematics.