The question you pose assumes that all the documents a professor has accumulated over the course of his/her career is worth permanently retaining in an archives. However, there are factors a university special collections/archives will consider when determining whether to (1) accept the archives of a professor and (2) to determine what in that professor's archives holds archival value.
All archives face challenges of space and staffing constraints. Most archives don't have the luxury of empty shelving awaiting new fonds (a person's archives), and the nature of archives and archival operations makes it difficult to weed out materials (deaccession) that have already been formally acquired by an archives (archival principles such as the archival bond and the principle of provenance, and administrative hurdles such as donor agreements are some of the challenges to deaccession). Most archives don't have the staff hours necessary to process and provide access to the materials it accepts. This necessarily limits the number of faculty fonds a university archives can accept, so the archives will have to consider, amongst other factor, the relationship between the faculty member and the university and the contributions the faculty member has made to his/her field when deciding whether his/her fonds will be accepted.
If the faculty member's fonds is accepted, the archives will need to conduct an archival appraisal to determine which records hold the most archival value (which records provide evidence of significant transactions, which records contain the most informational value, etc.). For some records, laws on privacy make deposit in an archives unfeasible—in most jurisdictions, legislation places additional requirements on protection of privacy in medical and student records (in the United States, for example, these areas fall under HIPAA and FERPA, respectively). Some records duplicate information found in another record in a more efficient or effective form (final versions vs. drafts, or a course syllabus that describes major assignments, rather than the description sheets for each assignment).
Archival appraisal is always a balancing act between a desire to preserve the integrity of a person's fonds while recognizing an archives' inability to preserve everything and there is no international standard available to guide archivists on how to proceed. Indeed, it's an area of archival science that is fairly contentious.
To think about how few of the records created by an institution end up in an archives, in most national governments, only about 5–10% of the records created by the government will make it into the country's archives. On a more personal level, think about your desk. Would you want to preserve every piece of paper that is on your desk and every file you have stored on your computer? You'd probably want to do some weeding before giving your records over to an archives.