Private schools generally treat FTs as if they are a dime a dozen; that is, along with being easy to scam, they're also easy to find. Unfortunately, they're right.

Apart from what you've said above,I fully agree with what you have written.
As you well know,China is a country of many small cities.Teaching in one of them gives you much more job security and freedom in the classroom,simply because it's impossible for employers there to replace you timeously by seeking other FT's locally to teach your students by taking jobs on the side.So,even if you're not so popular for whatever reason(s),you'll be treated well;as the old adage goes - better to be a big fish in a small pond than a small fish in a big one.
But of course,in many of the less-developed places,foreign foods are either unavailable,or massively overpriced if they indeed are.Plus the night life there is probably much inferior to that of big cities.Also.you may find it hard to meet more than one or two other louwai,simply because there aren't any to be found locally.But that's not necessarily a bad thing!
I've taught at two private schools and four public schools in county seats,as well as private and public ones in big cities.Give me the small city everytime - your Chinese colleagues will likely be less picky and arrogant than their big city counterparts.And your students will probably behave well and be more inclined to study.