Any commercial pilot would not bat an eyelid at telling ATC that 'thanks, but I'm staying here rather than going to little piddlington'.
Many PPL pilots view Air Traffic as being the sky police and would feel a lot of pressure to bog off to somewhere smaller if it were suggested/requested.
The ideal scenario is one where during training the student is made aware that, all things being equal, cause a problem at little piddlington and not major international.
Until you've been up there, scared and wanting to be on the ground you might not have the correct empathy setting for dealing with a light aircraft pilot in distress.
Cheers
WWW