It's a tricky one........
If a school is going to judge a child on their hair style then do you really want your child to attend that school?
In an educational environment you would hope that the school, interviewer or decision maker is able to look past appearance and judge a child on the interview, sports performance,exam result, headteachers reference etc
There have been so many examples of schools that have been prejudice/ strict towards pupil's hairstyles, uniform etc and those that have come to the fore as they are state schools.
The ones you list are independent, privately funded and get so many applicants that they are able to pick and choose and really there is not much in the way of recourse........ so it's a different kettle of fish.
First impressions count! and in primary schools they are much more lenient regarding these things, but most of the schools you list in your post seem quite traditional and i am guessing have strict uniform and appearance policies?
When you did school tours/visits etc did you see any children with hair the same length as your child?