The problem with this question is that there are too many variables.
A university degree in a subject like computer science will not significantly increase a native Japanese speaker's kanji vocabulary. A degree in biology or medicine will add some, but a degree in philosophy, history, or literature could potentially add thousands of rarely used (outside of that specialization) characters.
There's also a huge question about "what does it mean to 'know' a kanji?" Even very common characters have unexpected readings.
How often a person needs to look up kanji varies depending on what they generally read. There are some lists of kanji for particular contexts, but even those are usually too high-level to be of much 'use'. An American who habitually reads "The Economist" is much more likely to need their dictionary on a regular basis than one who just watches the nightly news.
(I've marked this as CW to avoid gaining rep for what is essentially an extended comment complaining about the question, rather than an answer)