Are the ICAO phonetic numbers used anywhere?
Is there any country, military, or agency that regularly uses the full ICAO (NATO) approved phonetic number pronunciations? Is it taught to any pilots?


Yes, pretty much every country in the world. As you mostly have experience flying in the USA, where the native language is English, you may not be used to hearing these pronunciations so much. People whose native language is English tend to pronounce words [and numbers] as they would in normal speech. In most of the world, however, English is by no means the native language, so controllers and pilots alike will use the pronunciation guidelines created by ICAO to ease understanding across multiple dialects and accents.

As an example, the Danish aviation regulations has an exact copy of the table you present in your question, and it is used by everyone.