There's a 4th School of thought as well.
They optimize their hardware to certain heavily colored ( Wow factor) version of distortion that the SQ becomes 'relatively' independent of the Source and Room. Whatever the garbage source material you input, irrespective of the room; the the sound output is just a variation of their heavily colored version ( mostly rounded HF, lush vocals and likable bass). You are least bothered about what the artist had intended, least bothered about the flat uniform accuracy of the response ; but the end user gets a beautiful SQ response.
The emotional tonality (it appeals more to heart, than brain) is so appealing that you tend to overlook the Non puritan expression of frequency spectrum, and just focus on listening more. It's the listener and his subjective preference takes a center stage instead of what sound engineers or recording artists would have preferred. For people who like that kind of SQ response it achieves a cult status, with most loyal brand following for every device in the chain. Well, by this time you know what brands I am talking about. Though pricey, They don't delve too much into specifications, their system set-up is overtly simplified and focus on initial wow factor which brings cash flow.
Finally, beauty lies in the eyes of beholder, So if the listener prefers this altered version of SQ ; his quest ends there. It's a great option for non objectively discerning listeners, which constitutes 90% of the population. Let the puritans crib, objective evidence seekers throw tantrums, but that hardly matters. In reality most of listeners probably crave for their version of this altered reality but our thinking brains puts hurdles in accepting the fact. Remember music is an artistic & emotional extravaganza not a Scientific one!