I am going through the uni application process currently, for the third time - not me obviously, but my children. In fact, dd is at this very moment 300 miles away with dh, visiting a uni tomorrow. Last weekend, I took her round 2 and we informally visited a third, picking up ds2 at the end of his term.
No it is not critical, it is not mentioned on the UCAS form, and yes, some schools can be very awkward about letting students have time off to visit. I know our school only allows 3 days, which is enough as most unis have an open day over the weekend, but it can be hard if, like my dd, you are hell bent on going to a uni as far away as possible and you need 2 days to travel there and back.
Ds2 is at an extremely high profile uni and he did not visit it beforehand. I think he attended an applicant day there, but that was after he had applied and been offered a place, and then chosen it as his first choice.
That said, they are useful though. Having visited 2 unis last weekend with my dd and having sat through all the same sort of talks for the same degree, both dd and I came away with quite clear views on the 2 unis in question. You get a feel for staff, courses, and of course the environment, as well as having the opportunity to ask quite specific questions. I don't think much of that would be attainable from a prospectus.