As the altitude increases the partial pressure of the oxygen decreases. Above about 14,000 ft. there is not enough PPO2 to keep a pilot fully functional for more than about 30 minutes. As the altitude gets higher, the time that it takes to incapacitate a pilot or passenger shinks drastically to a few minutes around 25,000 ft and if a plane were to suffer a sudden decompression at 35,000 feet a pilot would be concious for only about 7 seconds. At and above that altitude at least one of the flight crew is required to remain on oxygen at all times as there would not be adeuqate time to don a mask if a rapid decompression occurred. This is essentially what happened with Paine Stuart's chartered Lear jet several years ago. The passengers and flight crew were suddenly incapacited and the plane flew on by itself with the bodies on board before crashing a few hours later in South Dakota.
At those altitudes you also need a pressure demand mask that can maintain a bit more positive pressure than ambient pressure. And even then you are just buying more time. At altitudes much more than 35,000 feet even pure O2 in a pressure demand mask is not adequate to prevent hypoxia as the partial pressure is too low to allow for an adequate transfer of 02 in the lungs. Above 35,000-37,000 ft either a partial or full pressure suit is needed for anything other than short exposures in an unpressurized cabin. So in the event of a rapid cabin depressurization at high altitude the drill is to make a very fast emergancy descent to a lower altitude where the passengers and crew can breath.
The standard cabin pressure altitude of 8,000 ft is sort of a compromise. It is an altitude that nearly everyone can tolerate without oxygen for extended periods and the yet it reduces the pressure differential that needs to be maintained by the pressure cabin. The higher the pressure in the cabin, the more structure is required to maintain the integrity of the cabin, and more structure means more weight and less payload.
The designer of a commercial airliner needs to design the cabin to withstand the stress of a pressure differential sufficient to maintain an 8,000 ft cabin altitude at the maximum cruising altitude of the aircraft. In some turbocharged and pressurized light aircraft where weight is a much more serious concern, a pressure differential of only a couple psi may be used to keep structural weight to a minimum and the cabin altitude may be well over 8,000 feet when the aircraft is cruising at 20,000-25,000 ft.
Climbers also often use oxygen but due to the need to carry everythingup the mountian it is reseved for use only on and near the summits of very high mountains. Climbers who are scaling very high peaks also acclimiate themselves over a period of several weeks. There bodies adapt to the lower PPO2 and a properly acclimated climber can function for fairly long periods up to a maximum of about 25,000-28,000 feet where a non acclimated person would lose conciousness in a minute or two even at rest.
Above 28,000, even a well acclimated climber is just going to be slowly dying and at high risk of pulmonary and cerebral edema as well as hypoxia. At best a climber can tolerate that altitude for 2-3 days.