Talk to a secretary. I have known many. They still have to do typing tests as part of their interviews, as do stenographers. Since these skills directly speak to their vocations, and are fairly easily measured, it's natural.

Coders, on the other hand, aren't applying for typing positions. You could say that the "Draw the Pirate" tests, given by many companies, these days, are like typing tests (but I don't think so. I won't go into my thoughts on that).

I have heard, anecdotally, of programmers being tested for speed of coding, as part of the interview process.