Are you suggesting one open day to only one University? This will obviously work for some, but you need both a high level of ability and a high level of confidence?
(It was a tactic we sometimes saw used by very bright and ambitious kids, often those aiming for Oxford PPE and the Oxford Union. In Yr 13 they only applied to Oxford, as they intended to take a gap year and reapply if they were not successful. They did not want to reduce their chances of Durham or UCL as a fall back by applying first time round and then turning down the place.)
I would urge some caution. There are big cultural differences. DD went to one open day dominated by large family groups: OK medicine at QMUL. She felt she was the only one on her own, which she found off-putting, made worse by the fact that only fathers seemed to ask questions and the narrative given by the University seemed aimed at them (We are more academic than Cambridge, etc).
This is probably unavoidable. When doing the tour she asked others why they wanted to study medicine, only to discover that what and where to study was clearly a parental decision. She found it next to impossible to find out answers to her questions about sport and the extent to which students mixed with non-medics etc. It could be worse. An Asian friend, who is both Westernised and high powered (she headed a department in a major Asian University, has received an significant American honour and is now an emeritus Professor and in high demand for conferences) moaned to me that her FiL chose what her sons would study. One has Aspergers, something that is not able to acknowledged, even within the family, so the FiL failed to factor it in and the whole thing has been a disaster.
It is known that Oxbridge wants to encourage BAME applicants. I can quite see why GS's daughter with several siblings who have attended Oxford, has no problems attending an Oxford Open Day on her own, but can equally see why BAME groups might want to view the University as a family. There are lots of decisions to be made. Will the student fit in, will the parents feel sufficiently comfortable about the child living away from home, is it worth it, when a student could equally attend somewhere within commuting distance (possibly a good London University) at a lower cost.
The same will apply to others, including those with Aspergers, medical needs, Jewish students whose parents are worried about the growth in anti-Semitism, and so on.