There are two objective facts:
1) the current air temperature
2) the current air speed
These two facts can be combined to create a 'windchill temperature' for a naked person where the rate of heat loss from the naked person is the same at the same windchill temperature regardless of the air temperature and air speed. This windchill temperature can be normalised to a wind speed of zero - so if the windchill temperature is -10 C, then the naked person feels the same heat loss rate at 10 C and zero wind or 5 C and some wind.
All of which everybody is fine with.
Given that people don't climb naked, or with whatever assumptions the calculation is done by whoever has generated the windchill temperature, the windchill temperature is not correct for a climber (certainly not for a climber wearing windproof clothing). A climber entirely ensconced in windproof fabric would feel (almost) no wind chill effect at all.
Consequently saying at 'the wind chill temperature is -15 C' is irrelevant for a climber - it is highly unlikely that the climber will have the same rate of heat loss that they would at -15 C in still air. Consequently while it might be _qualitatively_ useful, it is _quantitatively_ hideously inaccurate.
I understand the point about exposed flesh but having a little bit of exposed flesh feeling the wind is not the same as the whole body feeling the wind; the warm windproof-protected core should keep the hands (for example) warmer than you would expect from that windchill temperature.
It's not that windchill doesn't exist, just that a 'windchill temperature' will always be an overestimate of the cooling rate for a windproof-protected climber.
Post edited at 13:02