Our Himalayan "Connection" shows 5 sites with Sagarmatha and Valley of Flowers being the "high altitude - natural" representatives. But the Western "Himalaya" (and the various names under which the ranges there are stricty known - Pamirs, Karakorum etc) is not well represented. Among the "Himalayan" (in the broad sense) countries Pakistan's T List consists of a pretty uninspiring list of Mosques, Tombs, Rock Edicts and Forts (isn't Rohtas enough!!!!) plus 1 Port - not a single "Natural" site! Nepal is much the same with a list of archaeological and religious sites. India does have Kanchenjunga (plus Hemis in Ladakh as a cultural site). Bhutan famously hasn't even got a T list. China has 1 Tibetan "mixed site" and Tajikistan has a proposal from the Pamirs. There certainly seems to be a reluctance to put forward "Natural" sites. I wonder if experience of IUCN assessments has a part to play? Is it harder to manage such a site (or at least to "pass" the required tests)? One wouldn't have thought that buffer zones etc up there would be a problem. Perhaps the political issues of Kashmir and Tibet play a part. Perhaps it is indicative of what these countries "value". I have elsewhere mentioned that a country's Inscribed and T lists can tell you quite a lot about how that country sees itself and wants to project itself to the World. The Pakistani list is perhaps worryingly uni-dimensional??
The scenic/geological value of the Karakorums is certainly very fine. Unfortunately I didn't go as high/central as Concordia (Though in Sagamartha have been higher to Everest Base Camp) but have been to Gilgit/Skardu. I still treasure a photo of a sign on a cliff face stating "Here Continents Collided"! (ref Meltwaterfall's comment about Plate Tectonics). There are certainly many less worthy mountain sites from around the world on the lnscribed List - this one is well worth our consideration.
As for making it a "mixed site" or even a "cultural Landscape" - I am not sure. The Sherpa way of life isn't represented with Sagamartha - but it was of course inscribed pre "Cultural Landscapes". I always feel that trying to mix too many things into a single site is a sign of weakness and lack of focus.
PS Sections 6.3 and 7.4 of this "Filling the Gaps" document re Mountains from IUCN are relevant. http://cmsdata.iucn.org/downloads/mountains.pdf
Interestingly among 28 potential "Palearctic Realm" mountain sites none is identified from Pakistan/Karakorum - though it does state
"Central Asia contains the highest and most extensive mountain areas on earth and most of the ranges (Karakoram, Kun Lun, Hindu Kush, Pamirs, and Tien Shan ) have, as yet, no natural WH sites!"