Why aren’t students tested on their word processing skills?

What skills are you looking for here? Who even knows what a tabstop is these days, much less how or why to set them. Hanging indents? No way.

But my 6th grader writes reports and what not. Those are going to be mostly done in a word processor. 20 years ago, when I was in college, I wrote a lot of documents in a word processor too; I'd be surprised if that has changed that much; my school wasn't hardcore enough to indoctrinate us in latex, I think everyone used Microsoft Word.

> Why aren’t students tested on their word processing skills?

It depends on the educational system.

> Wouldn’t teachers want their students to be able ... write up a document

It depends on the teachers.

In the early 2000s, I had a similar question nagging me: Wouldn’t schools want all their students to have digital skills?

Fast Forward to 2022, the simplest digital skill (= word processing), is still (as your question prove) an issue (in the US?).

We were in the 90s with "computer" classes. At least in some states/school districts in the US. I skipped it and took computer science, but still had to show I knew how to do things I'd been doing for 5 years to fully exempt the computer requirement.

I think it's because of parents wanting a say in their kids' education. I, for one, do not want my kids indoctrinated into Microsoft products. Just like the US civil war, it's too controversial.