In response to [research output] The professor might have his or her name on plenty of papers, but never as a first author. Presumably, the papers will look good on the postdocs' and PhD students' CV, not so much on the professor's. Is that the case?

No. Being senior/last author on a paper is valuable, often showing who is the main supervisor [in non-alphabetic author order fields]. Being supervisor of successful PhD's and postdocs is a good thing of course.

Only having papers as middle author, however, can create the impression that you are someone who is mainly helping others, but not really doing or leading anything yourself.

In response to [research output] The professor might have his or her name on plenty of papers, but never as a first author. Presumably, the papers will look good on the postdocs' and PhD students' CV, not so much on the professor's. Is that the case?

No. Being supervisor of successful PhD's and postdocs is a good thing of course. Each field has its own conventions where the supervisor is placed in the author list (2nd author, last author, ...), which are usually familiar to people working in the field (or deciding about grants in a specific field). Therefore, being in the supervisor/professor position on papers does look good on your CV.