Once you have tenure, presumably you're never going to have to search for a job again. However almost all professors have a CV on their website, and fairly recent ones. Why? They already made it.
Everybody needs a CV to help others better know them.
I am not a professor, but I think even tenured professors may maintain their CVs so as;
- As an advising professor, they need to hire or accept research (PhD or masters) students,
- As a university professor, they may hire PhD graduates in form of postdoc positions,
- As a person working in university or industry, they need collaboration;
and for many other reasons.
They need an updated and maintained CV so as people who want to collaborate with them in a research project get know them, their research interests and their previous works or at least their educational background.
Research students need to read their CV to get familiar with their research interests and know their past PhD or masters students' projects. This helps them to better choose an adviser whose education and research background is so near to their academic interests.
These professors may also want to apply to get a project, they need a complete CV to introduce themselves to the project owners or investors.