I think people think that with a £9k pa tuition fee here, it's "cheaper" to study in the US. I don't think that's so, and frankly, I think you get what you pay for. And the US Government generally wants an upfront indication of parental finances. My long-term experience of working or having research fellowships in the US is that it is actually a highly bureaucratic society (I have a US SS number somewhere ...) -- far more so than the UK, actually.
You need to cost in return airfares, and shipping costs. Are they ready for extreme heat & extreme cold, on the East Coast and the mid-West?
You also need to warn an 18 yo that the drinking age in the US is 21, and a lot of colleges will be very very strict about this. Especially for an overseas student. It's a good way to be deported ...
As others say, the US system is quite different from the English/Welsh system, although it has similarities to the Scottish system. The main consideration s that the US system is huge and the choice can be baffling. And it's not really possible to do a variety of campus visits.
I'd be asking your child why they want to study in the US. What's the motivation? If it's adventure, what about a gap year project, Summer Camps USA or similar?