Not so sure about the last one, but, yes, illegitimately gained degrees should be (and usually are) revoked.
On the last one: if someone hid the fact that they committed a crime while a student that would have gotten them expelled, then I'd say that the degree was illegitimately gained.
And I'd also argue that who disavows science, promotes anti science or dismisses the scientific process should be barred from using their title. E.g. everyone working for AiG or DI.
I'm not sure how that would work; it's not like you need to get permission from a university to say that you graduated from there.
One option that might hopefully make both sides happy, though: when they issue a copy of your transcript - e.g. for a new job or to apply for grad school - it could include your disciplinary record, including any censures issued after graduation.
That way, it would be clear that the student did the course work for their degree, but it would also be clear that whether the person has done something to bring the institution into disrepute.
Employers who care about those sorts of things could ask for a fresh transcript sent directly to them by the university.