This comment briefly discussed the Greek idea of the noble savage and I was wondering if this was primarily a modern, European phenomena or if not, how common was this belief?
Piggybacking off of OP's question, was there a noble savage myth prevalent in Imperial China in regards to their neighbors on the steppes?
The comment you're referencing is referring to a different idea of the "Noble Savage". The modern version, which you're asking about, is as far as I know an entirely European view, used alongside racist views of non-European peoples to distinguish those groups which were higher up the scale of "civilized", and therefore were capable of being "tamed".
In some areas of the world, the indigenous people were beyond help. This was the case in South America, where efforts were made to convert the indigenous population but no efforts were made to civilize them. The conversion only served to protect them from hell in the eyes of Europeans, and was seen as a kindness.
In New Zealand, the Māori were viewed favourably by their British colonizers. At least, as favourably as non-Europeans could be viewed. They were seen to have,
[...] capacity for civilization. Indeed the Māori had the good fortune to be ranked higher than most other 'savages'. Exponents of the old theory of a Great Chain of Being invariably put the Maori somewhat above the unfortunate Hottentots or Australian Aborigines who were usually placed in the last links in the chain between man and the apes.
Even in newer forms of racial classifications of humans, the Māori fared well compared to others:
It was much the same if a more modern though still pre-Darwinian evolutionary scheme was used, for the Māori, [...] were usually placed on the border between savagery and barbarism and assumed to be capable, with proper guidance, of graduating to civilization.
Despite these quotes however, the Māori were never really viewed with the "Noble Savage" descriptor by the British - it was the French who had this idea. Marion du Fresne in particular subscribed to that view, and it cost him and twenty of his men their lives, when they assumed that the "nobility" of Māori would allow him to flout their laws. Laws which he viewed as lesser because the Māori were not civilized like Europeans.
So we can see the concept of the "Noble Savage" was inextricably linked with colonization, and a desire to rank ethnic groups into a racial hierarchy. It was used to separate those 'savages' who were beyond help from those who were able to progress. The attempt to civilize Māori through colonization was often referred to as a process of making "brown skinned Englishmen", which is rather telling - the idea that a group could be brought up to one level, while others couldn't.
I hope that's a decent explanation of it, and how it was applied in some areas of history.
Source:
How To Civilize Savages: Some 'Answers' From Nineteenth-Century New Zealand