Nick,
Several points to make here.
First, in relation to your general point, what you describe is the system here in China, work with it or get out.
Put yourself inside the mind of the parents. Most are busting their b*lls to pay for the education of their children, so of course they want to see native speakers teaching English to little Johnny or Jenny, (white face = native speaker) and dont they feel proud when they see a few words exchanged between a lao wai and their child. They feel vindicated in having made the not inconsiderable sacrifices to achieve a better future for their offspring, even though you and I know that optimism is often misguided.

Secondly: Most teachers in reputable schools in China are not backpackers. There is of course a small percentage of them generally utilized by chain schools and training establishments, but of the 30 plus teachers working in the two colleges in my area, there is not a single one. Extrapolate from that.

Lastly: having seen the level of English language skills displayed on this forum from Filipinos, Africans, pseudo Europeans, A'merkins and some Aussies, it doesnt in the least surprise me that parents insist upon native English speakers. However in my opinion none of the former qualify for that title as evidenced by the mangled spelling, grammar, syntax and woeful lack of language skill shown in this forum.

One small tip for you.
A basic rule in written English (taught in my first year at Junior School) states:
Never begin a sentence with And, But, So, or Then. It still applies.