I hope it's not me that's missing something!
I think a FL limit is appropriate for hypoxia because:
An altimeter is a barometer. It measures pressure plus how much you turned the sub-scale knob. If you always use the same sub-scale setting, you are only measuring pressure.
If everybody agrees on sub-scale setting to use, (which is 1013 by convention, but could be any agreed number), then everybody's altimeter measures the pressure in the same units. (feet, on a non-linear scale).
That means everybody can agree on an altimeter reading which was the limit for hypoxia, and it would correspond to an atmospheric pressure limit for hypoxia. Pressure is all that matters for hypoxia.
If the regulators specify a FL, they have specified an atmospheric pressure. It truly does not matter what the altitude is. The lungs do not care.
As an example, let us say we are at FL100, which is approx 700hPa if memory serves. That 700hPa is all our lungs care about.
Very roughly, 100hPa in the lungs will be CO2 and water vapour, 120hPa will be O2 and 480hPa will be N2. That adds up to 700hPa. The 120hPa partial pressure of oxygen is all that matters for hypoxia.
You will notice I have not mentioned the altitude yet, and that is because it doesn't matter, except as a rough indication of what the pressure might be at that altitude.
If the air below us is very cold, and QNH is very low, we could be at 8,000 ft. What do our lungs care? They are breathing in air at 700hPa. The O2 partial pressure is still 120hPa.