Why would you not want to be using a rendering library?

Because it's just not very useful in some contexts. I've seen web extensions which mostly query the current page, and it doesn't render much or even anything.

Not all pages are SPAs either. Many apps are the old request-response with some dynamic behavior sprinkled on top. jQuery covers that well.

This model is also quite compatible with the rising HTMX where the state/rendering is driven from backend and you just insert few dynamic pieces with JS.

document.querySelector("#element").classList.toggle("hidden")

There's no difference between document.querySelector("#element") and document.getElementById("element"), they're both same level clunky.

Also, what you wrote is not functionally identical. $el.show() is idempotent, the el.toggle("hidden") is not (as the name suggests, it toggles a class). It also needs an extra boilerplate class.

I could see not wanting to use a rendering library if you’re building a simple site on top of basic static HTML, but that’s not a serious discussion for industry professionals

There are plenty of non-professionals doing web stuff and I think it's great!

jQuery is such a heavy dependency for saving some characters

jQuery is 24 KiBs (minified, gzipped), that's a good price for the egonomics it provides. If you're constrained, there are API-compatible alternatives like cash which go down to 6KiBs.