Why do some professors not post their long list of publications? I notice that some professors -- some are now professor emeritus and aren't active in research anymore -- have an essentially blank faculty webpage, only listing their phone number and school address and office location.  What would be typical reasons for professors to leave their webpage blank instead of listing their publications?

Is it a desire for privacy?  An indication that one is no longer active in research?  Disgruntled feelings about academia?
Your question contain several implicit assumptions that make the question difficult to make a generalised answer.

Firstly, the use of web pages for university faculty varies from country to country and institution to institution. There is no generalised understanding of what a university or faculty members web page should contain, and this is often influenced by cultural norms. Further, this can vary from discipline to discipline. Some academic areas value public lists more than others - academia is such a broad church.

Secondly, you seem to be assuming that professors may have any control over the content of their web pages or published academic profiles. In some places they do, and they may be free to edit them themselves. In some places these are centrally controlled and populated from some form of content management system database. In some places these are managed by a marketing department as part of the institutions advertising and public relations; further some places might use an external public relations agent to populate the pages.

Thirdly, you underestimate the amount of internal politicking and petty squabbles that go on inside large institutions like universities. Professors, particularly senior ones, go in and out of favour like pop chart hits. It is not beyond the bounds of pettiness for someones entries to be deleted out of spite and recognition of their unfavoured status. Their existence cannot be expunged, but their bibliography can be.

Fourthly, you assume that universities have a degree of capability or competence. In my experience there are plenty of incidents university staff (support or academic) being incapable of rendering edits to obviously incorrect profiles.

Fifthly, you assume that perhaps everyone there actually cares about it. Perhaps the professor or the support staff don't really care about this particular part of the profile and have no plans to change it.

Sixthly, you assume the professor or the faculty actually know that the list of publications is missing. In a large institution with many many faculty; even in a caring place, it is possible for errors to slip through unnoticed. Not every faculty member would be egotistical enough  to regularly read their own personal profile.

There may be more reasons, but that list should do for starters.