OP,
Since your DC wants to do it, saying no also has risks.
If you want to guard against the random bad experience angle, you have to get DC to do at least 4 or 5.
I would also suggest that the best fit school be one of the last schools visited.
I think the random bad experience is most likely to happen the first time when DC doesn't know what to expect or doesn't know what to do if offered alcohol or something similar.
If they have been to 3 or 4 of these, they will be more comfortable with the experience.
As someone else suggested, you can do the first one with someone you know at a school not too far from home, just to get the feel for it.
Then do a couple further away with someone the college suggests.
If your DC doesn't want or doesn't have time to do 4, explain that doing only one won't give them anything to compare and suggest that without anything to compare little new can be learned and maybe the visit isn't necessary.
Good luck