A million years ago when I was applying for universities my parents had no involvement at all and we would all have laughed ourselves silly if there had been any suggestion that parents should come with their teenagers to interviews, open days etc. However, times have changed and it's not just because we're all helicopter parents now. Most students have far more financial support from families, apart from anything else. I think it's useful for the student to have someone to compare notes with - not essential, but it is after all a massive decision to make when you're only 17 or 18, because of the financial implications.
We went with our daughter to a UCAS day at Reading because she has Asperger's and wouldn't really have been able to get there on her own. We found it very illuminating. The department laid on some joint talks/tours and then session where parents were hived off for a talk aimed at us while the students did something else. The assumption seemed to be that most students would have one or both parents with them, and that was certainly true of our group.
(She didn't go to Reading in the end - but not because of the UCAS day, which made a very good impression. She's studying part-time at Birkbeck instead and living at home, which is working out well. We went to the pre-application open evening there with her as well, and saw another young woman accompanied not just by parents but also by grandparents!)
Son is off to a UCAS day at UCL soon and his dad is going with him, as much out of nosiness as anything (we both went to UCL, but we didn't do History).