A UK school can be a cheap option for full pay families compared to equivalent US schools, for example Oxford would be about half the price of top US private colleges (partly because most courses are three years), although note that lab sciences/engineering/CS costs more at some universities.
Secondly, the admission standards are more test driven, there’s no need for ECs and GPAs are generally ignored (direct consideration of race is also illegal). So a kid who is not so outgoing or who is very smart but has struggled with ADD (impacting his/her GPA), will usually have a much better chance of admission than at equivalent but more “holistic” US schools.
Thirdly, overseas fees are very attractive to universities (other than Oxbridge), making it easier to get in for overseas applicants compared to domestic students. The process is very simple and cheap, one application for 5 universities (actually 5 courses), one personal statement and one recommendation (albeit not the same content as for US schools).
So to take an example, a kid might choose St Andrews because they can’t get into UIUC, or Oxford because they can’t get into Princeton, and they might well have a lower total cost in some cases.
You do have to consider that the courses are more specialized, particularly the three year courses common in England, where there are no electives outside the major or general ed courses. And you can’t change without starting over. So you have to be absolutely certain you want to study the subject you choose.
I would be cautious about any majors that lead directly to a professional qualification in the US, like engineering. CS is more transferable, though internships may be harder to secure.