Completely agree that in the UK there will usually be a coordinator who knows how to write these references and can do them quickly. The problem in the US is that the counselor won’t and is unlikely to have the time to figure UCAS out if they are dealing with potentially hundreds of other students (our public school has one counselor for 400 students, 100 per year). Perhaps some private schools might have the resources to do this.
So a trusted teacher may be of more help - S was fortunate enough to have a history teacher he was close to who had done a master’s degree at Oxford, I believe @HazeGrey’s S also had a teacher who had taught in the UK.