But what's the point in acknowledging numerical issues outside of [-1,1] if polynomials do not even work there, as author explicitly notes?
The author does not address the single most important reason why high degrees of polynomials are dangerous. Which is pretty insane to be honest, obviously to be honest you have to at least mention why people tell you to be cautious about high degree polynomials AND point out why your examples circumvent the problem. Anything else is extremely dishonest and misleading.