10K is excessive but sounds like a family choice. Certainly not the norm. Our general rule has been to have a mix of tours pre-application that is targeted and helps narrow the field as well as honing in on what exactly the kid wants in a school. The child does not have to vist all before applying but if they haven’t then the interest has to be quite strong to justify the application as to us, acceptance then means a visit and travel does add up. For far away pricey travel though, a visit post acceptance simply makes more sense to us. We combine visits into geographical areas and will leverage family to stay with when we can, flight deals, planning somewhat far out to get better prices. It’s been a mix of family trips and just the prospective student with one child.
I do believe they are critical. We just returned from one (total cost for our family of 4 was maybe $800 and combined a spring break trip, small vacation, family visit with 3 schools. Long days, lots of driving but very very worthwhile both in terms of those 3 schools but also in how the student felt about those, impacting the rest of the list. That said, even with one kid and parent, hotel, rental car and flights can add up so you need to be selective in what makes sense. Narrowing the field with local visits is very very worthwhile before spending bigger dollars on schools farther away.