The problem is the pressure, only 26% at 10km of what you have on ground. Oxygen getting absorbed in your lungs depends on that pressure, less pressure, less oxygen gets to your blood.
No, oxygen getting absorbed into your lungs depends on the partial pressure of oxygen in your breathing gas. Partial pressure is the pressure multiplied by the percentage of the gas in question.
At sea level, the partial pressure of oxygen, ppO2 is 0.21, because the pressure is one atmosphere and the air is 21% oxygen. You can obviously survive just fine on a ppO2 of 0.21. If you're in an environment with 0.26 atm ambient pressure and breathing air, you're getting a ppO2 of 0.26 *0.21 = 0.05 atm. Generally, 0.16 atm is considered the minimum safe ppO2, though that's a pretty conservative number. But 0.05 is not enough to keep you alive. If you're breathing pure O2 at that pressure, though, the ppO2 is 0.26, which is higher than the ppO2 of air at sea level, so you'll be just fine (as long as you avoid freezing to death).
Incidentally, SCUBA divers worry about excessively high ppO2 levels, because oxygen is toxic. Generally, divers try to keep their ppO2 below 1.4 atm, which means that breathing air becomes dangerous at depths greater than 220 feet (of course, at those depths the ppN2 of air is generally already having a huge narcotic effect so diving that deep on air is a bad idea for other reasons). For deeper dives, therefore, divers use gas mixtures with less O2.
Such deep, technical, diving is pretty rare, though. What's very common is diving with air that has been enriched with additional O2, usually to 32% or 36% O2, called nitrox. The purpose of this is to lower ppN2 levels during the dive, to reduce nitrogen absorption by the tissues and therefore increase the amount of bottom time without needing decompression stops to safely offgas the N2. Many divers also think the higher O2 levels make them feel better during and after the dive. However, with 36% O2 (EAN36), ppO2 reaches 1.4 atm at only 128 feet so divers breathing nitrox have to be careful to stay shallower. Smart Nitrox divers test their breathing gas O2 percentage before every dive and calculate a floor below which they must not go.
For example Mount Everest climbers, if they just ran from 0m to top of Everest they would pass out, extra oxygen or no.
The top of Mount Everest is about 0.33 atm, which means a 100% O2 mixture would provide them with more oxygen than they get at sea level. The reason they have to acclimate first is that carrying enough O2 to breathe 100% O2 is impractical. It would require carrying thousands of cubic feet of compressed gas. By acclimating themselves they increase their bodies' ability to utilize lower ppO2 levels. Depending on their fitness levels and degree of acclimatization, they may be able to get to a point where they don't require supplemental oxygen. Most, though, will need some.