Stravinsky's hugely successful career took a nosedive in his latter years - when he succumbed to the pressure to write dodecaphonic twaddle.
I agree with the first part of this but not the second; where is the evidence that the already "hugely successful" Stravinsky (as he undoubtedly was) was even pressurised (externally) to write dodecaphonic music, let alone that he "succumbed" to such "pressure"? Surely this was his decision alone, not one imposed from the outside? - and the mature Stravinsky never struck me as the kind of composer to take his orders from elsewhere!
Twelve-tone composition is simply an intellectual diversion, rather like doing sudoku puzzles. And performing it is rather like giving a public display of sudokus which you have solved.
I don't see why it needs to be, or indeed why it should be regared as presumaing any greater degree of "intellectual exerise" than writing music in any other ways; one might as well seek to posit a similar argument about the intricate disciplines of species counterpoint as espoused by Renaissance composers but I cannot see that gaining much acceptance.
The actual continuum of twentieth-century composition - Janacek, Strauss, Lutoslawski, Ives, Britten, Tippett, Shostakovich, Prokofiev - has no space for the intellectual affectation of twelve-note composition. Its influence is a complete 0.
I would be as wary of underestimating over indeed overestimating the influence of 12 note serial procedures and practices as I would of claiming that, notwithstanding their importance, the eight composers whom you mention are representative of the entire "continuum of twentieth-century composition" when clearly that "continuum" is vastly wider and richer than just those; to add in Sibelius, Varčse, Nielsen, Carter, Xenakis, Messiaen, Henze, Bartók, Berio, Pettersson, Sessions and a bunch of British symphonists from Vaughan Williams, Brian and Bax through Rubbra and Walton to Arnold and Simpson up to living ones such as Maxwell Davies, McCabe and Matthews alone illustrates that.
Of course, it's placed on a pedestal by the self-appointed priesthood of 'modern' composers.
If its influence is "0", how has it gotten and stayed on that pedestal?
12 note serial practice is just one of the ways to salvation that has no appeal for me (and when I write 12 note themes I do not treat them serially), but we don't (thankfully) all go the same way home. Furthermore, hardly any listeners would be able to tell just by listening that a piece is written using 12 note serial procedures in any case.
