Urban public schools are wholly different. Some of them may well be best served by TSA style pat-downs.
If I were a stereotypical, middle-class parent - which I will never be - and I had a child in a school that utilizes such security measures, I would assume one of the following:
1. The school is a dangerous place full of junior thugs and there is a semblance of a genuine justification to these measures. This is not conducive to a good education for my child, nor to his/her/its safety or future development as a free citizen.
2. The school is not a dangerous place, but is run by paranoid control freaks. his is not conducive to a good education for my child, nor to his/her/its safety or future development as a free citizen.
3. Both of the above are true.
Note also that the quality of schools is known to be a factor for parents' choice of address.