Should I mention teaching experience in my cover letter? I am applying for tenure-track positions in R1 (say, top 50) universities in Computer Science in the US.

When writing the cover letter, should I mention teaching experience and competence?
Or should I leave it for the teaching statement?
I've been on the faculty recruiting committee of my American R1 top-whatever computer science department for more than 15 years, including three years as committee chair.  (But my experience is only in one department, so take this with a grain of salt.)

To first approximation, nobody will read your cover letter.

It's quite common to get faculty applications that have no cover letter at all, or that include a plain-text email "cover letter" that reads "I'm applying for an assistant professor position; I've uploaded the requested documents and the contact info for my references.  Kthxbye!"  I have never seen this affect discussions about who to interview or who to hire.  Nobody ever notices.  Nobody ever cares.

All the information we care about is already in your other application materials, your recommendation letters, and your papers.  In particular, recruiting committees already expect to see a detailed description of your teaching experience in your CV and in your teaching statement.  That's where everyone puts it, so that's where we look.  And we'll look there regardless of whether you mention it in your cover letter.  So why would we look at your cover letter?

In my experience, cover letters are only useful if they contain information that potentially changes the hiring process — like "I am applying for a tenured position at the rank of full professor." or "Please keep my application confidential." or "My spouse is also applying to your chemistry department."

Cover letters do play a more important role in some departments, because they want convincing evidence that you are seriously interested in a job there.  After all, if you're just shotgunning your application to every ivy-colored building in the country, then interviewing you is probably a waste of their time and money.  But this is much less likely to be a concern in a top-50 R1 department.  It's never been a concern at mine.