I think the breakdown is simple: Collectivist vs Individualist.
These folks are pushing team effort rather than personal effort. These folks are pushing Collectivism. The Bolsheviks and the Nazis and the Democrats are smiling.
Yes, and don't forget the early Adlerians, including Adler, were socialists. They had good intentions but had a flawed perception of human nature. Socialists, one and all, believe that humans are born as a "blank slate" and they can made into almost anything those who are influential desire. This is nonsense.
The educators following this have no evidence that it works just a leap to faith that it must on the basis of their conception of human nature. Children will not quit competing any more than adults. They might also take their competition to the moral realm like the socialists and compete for "moral superiority."
Both suppressing ordinary competition and expressing moral superiority are the hallmarks of the current educational system. Remember, the moral superiority is not based on religious convictions but rather environmentalism, affirmative action, multiculturalism and so forth.