The problem with high altitudes is not the lack of oxygen, but the lack of pressure. At lower pressures, your lungs are less effective at getting the oxygen into the blood. Oxygen masks on airplanes increase the amount of oxygen in the air you breathe, which helps the lungs to absorb more even in low pressure.
In a typical decompression, there will be a gradual loss of pressure. However, by the time the masks drop, the pressure has already dropped a fair amount. There is no set time that it takes for pressure to drop. It could be very gradual, or it could be explosive decompression that happens extremely quickly. As a passenger, aside from the obvious explosive decompression, you will not be able to tell how fast the pressure is dropping. And because of how hypoxia works, you many not even be able to tell that you are not getting enough oxygen. So you have no way to tell how long you can safely wait before putting on your mask. Without enough oxygen, you eventually die.
So by not putting on the mask, you are risking death. What is the benefit of waiting to put on your mask?
Airlines operating under FAA regulations are required to carry certain amounts of oxygen, depending on the flight. FAR 121.333 covers the requirements for oxygen supply during an emergency descent.
For airliners certified to FL250 and below, they must carry 30 minutes of oxygen for 10 percent of passengers, but only if they can safely descend to 14,000 feet in 4 minutes.
If they cannot safely descend, or if the airplane is certified above FL250 (as most airliners are), there must be at least 10 minutes of oxygen for all passengers, and enough for 10 percent of passengers for the duration of flight with cabin altitude between 10,000 and 14,000 feet.
So the airline is required to provide at least 10 minutes for all passengers, more than enough for an emergency descent to a lower altitude. If they can't descend within that time, they must carry enough for the 10 percent of passengers that need oxygen the most for the duration of flight at those high cabin altitudes. There is no reason to wait to put on your mask.