>>2844611 (OP)
You run into additional issues with peaks that tall, mostly being that they start to just up into the stratosphere and get hit with jet stream winds. Everest and other 8000m peaks are mainly climbed during two specific weather windows to avoid the monsoon.
Everest is also close to the Equator. A mountain like Denali closer to the poles has thinner air as compared to a 6km mtn near the Equator because air buldges at the center.
With how far the sport has moved, I think a highly trained Alpinist (possibly paragliding from the summit to avoid descent) with cached oxygen (4L per minute lowers the elevation to 10k lower which is common to climb without O2) could go all the way up to 10km on a non-technical mountain near the Equator in an area without a constant jet stream and large blue bird weather window. Anything else and it probably isn't possible without jumping onto it via a HAHO jump or something.
