Unless I don’t understand what climbers are breathing up there, you would think that bottled oxygen would overcome the altitude. But clearly I’m missing something!
1) every bit of oxygen you need has to be carried by you, which is very heavy and limits the amount you can bring with you, so you have to conserve it and balance weight of the bottles vs. benefits of oxygen.
2) The main problem is that the air pressure is less. So even if you’re breathing pure oxygen, it’s going to be pure oxygen at low pressure, meaning the number of oxygen molecules you’re inhaling is a lot less than the number of oxygen molecules you inhale at sea level with every breath. So one breath at altitude, even if it’s pure oxygen, will contain a lot less oxygen than one lungful of air at sea level (air at sea level is only about 21% oxygen). So there’s a limit to how much oxygen you can inhale under that lighter pressure. You can inhale a full lungful, but that lungful won’t have as much oxygen.
And your body doesn’t absorb 100% of the oxygen you inhale. It only absorbs a fraction of it, limiting the amount of oxygen as well. Like, at sea level, breathing air, you inhale 21% oxygen and exhale 16.4% oxygen. I don’t know the equivalent percentages when breathing 100% oxygen, but the point is, you’re not using 100% of that oxygen.
If you wanted to inhale the exact same stuff you do at sea level, you’d need a pressurized space suit of some kind that would allow you to inhale at sea level pressure. I gather nobody does that because such suits are very heavy, very expensive, and you also have the issue of having to carry all that oxygen with you, which is too heavy.
This issue of pressure is complex and SCUBA divers face it as well. The whole problem with breathing underwater is that you need to breathe at the same pressure as what surrounds you. SCUBA converts the high pressure in your air cylinder into ambient sea pressure that is lower than that in the cylinder but higher than in the air. If you want to inhale air at sea level pressure by underwater, then you have to have a pressurized environment like a diving bell. Just like you need a pressurized environment at altitude like the space suit I mentioned above.
Can you rephrase your question? Are you asking what it’s like breathing from an oxygen bottle? Or you are you asking how altitude effects the bottle itself?