What’s the point of the rule of thirds?

I stumbled upon this old response on Threads from Jim Richardson—one of my favourite contemporary photographers—which I found via a link to an entirely different, and unrelated, post on that platform thanks to a comment on Reddit that I came across as a result of a search on DuckDuckGo. So much for avoiding internet rabit holes, but at least this time I was led to somewhere meaningful.

Commenting on yet another photography ‘tip’ discussing the rule of thrids, Jim asks—

You know, for every element of the picture that lines up with one of those lines, there are about ten things that don’t line up with anything. In almost any composition you can lay down those rule of thirds lines and something somewhere will fall under a line. And lots of other stuff won’t. Where is the value of this randomness?

Unless you have a blank sheet with a single dot that you can cleverly place along a third of your composition, this rule ‘fails’ pretty much everywhere else in that something or other gets placed along a line of thirds in favour of something else or, magically, a couple of things lie on those lines. Or you step back to force something to line along that grid forgetting your original intent with your composition.

This rule is great when you are lost and unable to dream up a composition; but you are better off not starting with it all the time because it has the ability to quickly takeover from your artistic intent.