My experience from an R1 university (research focused) is that most of the professors didn’t primarily want to teach, but instead to focus on research, while teaching was what they did to make their salary. They were usually happy to teach a few courses, and especially upper level courses focused on their area of expertise, but the main goal was getting funding to pursue research, and that usually comes from (or is distributed through) some public institution.
My experience from an R1 university (research focused) is that most of the professors didn’t primarily want to teach, but instead to focus on research, while teaching was what they did to make their salary. They were usually happy to teach a few courses, and especially upper level courses focused on their area of expertise, but the main goal was getting funding to pursue research, and that usually comes from (or is distributed through) some public institution.