Maybe Harvard. But I am employed as a math professor at a Research I state school, in which context you are quite mistaken. Research is most important, but good teaching is also important.
"Universities don't care about teaching" is a fun meme to kick around, and there are anecdotes to support this, but by and large it is not true.
My comment was directed more specifically to Harvard and narrow set of top tier schools, I do not believe that universities don't care about teaching. The list of "very high research activity" (apparently research 1 is no longer used) includes 108 schools [1] of which Harvard is at one extreme end.
That said, my father recently retired after 33 years with his department at a "high research activity", the second tier, and he can't recall a single case when someone was denied tenure where teaching performance was an issue. Research, and increasingly grant acquisition were always the issues.
Personally, I went to a small liberal arts school. Having taught at two top universities, private and public, I'm happy I went where I did. Undergrad teaching was the top priority and the difference is stark.
To play devil's advocate for a moment, the tenure evaluations I am familiar with at many universities take student feedback into account, as a proxy for "good teaching," but unfortunately teachers students like and teachers that are good at teaching may not be the same. Thus universities seem to care more about keeping students happy than about "teaching" per se.
"Universities don't care about teaching" is a fun meme to kick around, and there are anecdotes to support this, but by and large it is not true.