The above posts provide some fairly helpful, comprehensive and informative material about the "New Complexity" movement. A few areas remain open to consideration, however and I'd like, if I may, to start a few balls rolling...
Flynn is indeed not a part of this persuasion; nor is Zimmermann, although it should perhaps be understood that the particular Zimmermann under consideration here is not Bernd Aloys of that ilk (just for the benefit of anyone who might not have heard of the one referred to here) - I mention this as the mention of "Fox" appears to have caused some confusion in this thread and, while on that subject, it is perhaps worth noting en passant that the likely fictionality of the identity of "Jason" of that ilk appears now to be greater than it may once been (although if this is not the case, no doubt the real "Jason Fox" will emerge and tell us something interesting, accompanied by some supporting evidence, about himself and his work).
The apparent avowed aim of certain "New Complexity" composers to write music "where the TRUE music is from the struggle of the performer(s) as they try to play these monstrously difficult works" might, of course, be seen as inviting the potential risk of a problem in the longer term, in that challenges posed by a composer in a new piece may later become absorbed into players' technical disciplines to the point at which they no longer represent, or remain regarded as involving, the kinds of extremes that they might originally have been thought to embrace. Furthermore, this is nothing new, nor is it even the exclusive province of "complexicist" thinking; the "New Complexity" performers' struggles to overcome extreme demands of the physical/technical and mental/physical co-ordination type, though obviously quite different in nature, are very similar in principle to those challenges set down many years earlier by, for example, Alkan and Godowsky, the former expecting unprecedented stamina, velocity, leaps, etc. and the latter requiring the total independence of each finger. Finnissy indeed cited Godowsky as an example, however apparently indirect, of a composer who opened up the possibilities of multi-layered material within what an individual hand can play. Even before Alkan, Paganini had set down challenges for string players; some of these remain to this day at or beyond the extreme edge of what most players consider themselves capable of achieveing.
Whilst it is undeniably true that the vast majority of performers have not responded to most of the challenges set down by "New Complexity" composers, it is also true that, until relatively recently, a not much smaller majority omitted to address those of far greater vintage set down by such composers as Alkan and Godowsky.
The question of the extent to which listening to a "New Complexity" work with a score may assist understanding poses another problem; leaving aside how helpful or otherwise listening with a score may be thought to be for different listeners to different works, this practice will be of no help at all to anyone who is not already musically literate. If listening to such work with a score is (appropriately or otherwise) to be recommended as a useful - even essential - practice, should it be assumed that such music is therefore not for the ears of those unable to read scores - or, at the very least, that the musically illiterate will likely have greater difficulties in getting to grips with such music? If so, what should we think about that?
Another problem is that the participants in this "school" are, as has already been noted, very different to one another. Finnissy is particularly different, not only because he more frequently absorbs greater amounts of material from sources outside the customary expectations of "New Complexity" thinking than do many of his colleagues, but because he is (or at least was) also a much more active performer than most of the others; the significance of this latter factor is presumably obvious in the light of earlier references to the inherence and essentiality of the performer's struggles with this kind of writing. In more general terms, this overall problem serves to illustrate the shortcomings of trying to shoehorn a bunch of diverse composers into one grouping for the sake of the apparent convenience of labelling them as purveyors of "New Complexity". One could as easily challenge the meaningful validity of other "labels of convenience" in common parlance such as "modermism", "minimalism" and a host of like "ists" and "isms" beloved of those who seem to prefer to categorise rather than take each individual case on its own merits or otherwise.
Another issue here is the term itself. "New Complexity" does seem to be something of a misnomer - mabe even a double misnomer. Brian Ferneyhough - often cited as a kind of founder of this movement in music (for all that I doubt he set out to do any such specific thing) - was already writing works demonstrating his leanings towards "New Complexity" thinking almost four decades ago, with his first string quartet and Missa Brevis, so to continue to employ the word "New" in this epithet might seem rather suspect in the first decade of our new century. As to the the extent of the relevance of "Complexity", one must also address what strikes which performers as complex challenges, the reactions of listeners both literate and non-literate musically and the differences between these factors; one would naturally expect the performers to be more keenly aware of the various complexities in such scores than the listeners.
As to the question considered by Xenakis in the citation quoted earlier (which I am grateful for a reminder to re-read, as I have just now done) - and it is a question also considered by numerous other composers, especially in recent times - as to the position of the composer vis-à-vis his/her audience, what is often taken (by those who have not thought about it) as composerly arrogance is actually a practical inevitability, i.e. that no composer can ever be certain who will listen to his/her music where, when, or performed by whom or how adequately or otherwise, so it is simply not sensible for composers to "consider" - still less to hoodwink themselves into believing that they even can consider - their audiences when they compose.
Later in the same exchange, Xenakis is reported to have said "My problem is not to challenge the listener, no, no. To challenge myself, yes"; this, like so much else that he said here and elsewhere, is eminently worthy of serious consideration. In the present context of the "New Complexity" movement, we have so far considered the factor of its composers challenging performers (their intermediaries, if you like), but we have yet to look at their challenging either themselves on the one side or their listeners on the other. Perphaps this notion alone might now open the field for more contributions...
Best,
Alistair