Native Speaker Response
The same situation exists for the EU restriction on only EU members which blocks even native-speakers!!! However, I have taught in all continents except Australia & Antarctica, and have found the biggest problem with non-native speakers is that most do not do prepositions well no matter how long they have spoken English. Secondly, I can teach math as long as it is under 5th grade! Meaning, as long as I know more than a certrain level of student, I do fine, because they don't know enough to ask a question I cannot answer. I find that few teachers, native or non, can explain things well if it is complex grammar, etc. However, a well-trained native speaker has a better chance of doing so in my personal experience. Thirdly, brain research shows students learn best by listening and reading language rather than speaking (which reinforces mistakes --like a poor sports skill). Lastly, public schools are desperate and I cannot have one of those in your country...so go get one of those!