Personally, xenophobia plays its part here too. The most oft-quoted information, apart from the noise pollution aspects, concerns the foreign students/trainers which use the facility. Deep down, I think this has all the hallmarks of the old 'yellow peril'.
Anyway, to get Parafield to move, the advocacy groups would have to convince a federal court to overturn the 50-year lease on the property by Adelaide Airport. Good luck with that.
The two sites mooted are Murray Bridge and Mallala I believe. Nice drive out to both, to be honest, and as a local student, to continue my flight training, I'd be willing to make them. But gee, if I can avoid it....