CMD+C not working

Have you done a simple restart? That fixes many small nagging problems.

If a restart does nothing, try a Safe Boot and let it sit for maybe 5 minutes then restart normally and retest. Start up your Mac in safe mode - Apple Support

I've never seen this but obviously the web has as there er several old articles to be found.

If it were me, and obviously it's not, and this was that irksome I'd use the Recovery panel to reinstall the OS ... Command + R at startup. But then I've got several layers of backups, multiple bootable flash drives and a bootable clone so it's just not a big deal to me. This is your call.

Other's may have a less "severe" solution.

You can of course just live with it as it's a minor, albeit irritating, problem. I've lived with worse.

What indication do you have the it's not working?

When you highlight a file and invoke Command + c you don't see anything happen. The proof it works is in its being pasted when you invoke Command + v.