Boarding schools have always been for a minority and this hasn't changed because of foreign pupils.
Now, boarding schools are often keen on foreign pupils (esp. Chinese nowadays) because it IS actually good for their reputation: The Chinese education system is such that these pupils tend to ace maths and science subjects in exams and so the school can then market their outstanding GCSE and A levels results.
As for taxes: People who send their children to independent schools fund the public sector through their taxes in the same way as everyone else but do not use public sector resources at all. I think it is fair that they are not taxed twice on top of that.