Ah, but they can and do. A non-rebreather (NRB) mask with 100% O2 flowing at 12-15 L/min will provide about 90% O2 concentration to an adult. This is true even for the largest adult in severe respiratory distress.
There are a couple of reasons for this. First, the 3 liters figure you cited is the inspiratory reserve volume (IRV). Here are two definitions you need to consider:
Resting Tidal Volume (VT): This is the volume of air taken into the
lungs when you inhale. Tidal volume increases with exercise or
Inspiratory Reserve Volume (IRV): Total lung capacity minus the
volume of air in the lung at the end of a normal inspiration. This
means that we have a reserve volume that we can tap into as tidal
volume increases with exercise or activity.
Average capacities are 500 mL for VT and 3000 mL for IRV.
Note that the IRV is the volume of air that can be forcibly inhaled. It's not something anyone normally does except during extreme exertion (eg, athletics) or when directed in a breathing test. So the 3 liters you cite isn't the amount of air someone normally inhales; the TV of 500 mL is much more typical, meaning the bag provides two full breaths of reserve and the flow of 12-15 L/min O2 completely refills that bag every 3-4 seconds.
So a 1 mL reservoir bag being fed by O2 flowing at 15 mL/min is in fact more than adequate to supply 90% O2 concentrations to even a large adult in extreme respiratory distress. It can and will raise their SpO2 significantly in a short period of time if their cardio-pulmonary system is capable of absorbing and delivering it (which may not be the case if they're in need of such measures, but that's another issue).
Note that a NRB only works with a patient who is breathing adequately on their own. If a patient isn't breathing, or isn't breathing adequately, the next step up is a bag valve mask.
A BVM allows a medical provider to mechanically breath for the patient. The tubing you see coiled up next to the reservoir would be attached to an O2 source delivering 100% O2 at 12-15 L/min and then the provider would squeeze the bag at a normal breathing rate, forcing O2 into the patient's lungs. With this device O2 can be forced into the lungs of a non-breathing patient, or assisted into the lungs of a patient too sick or too weak to breath normally on their own.
Generally, once a BVM has been employed the next step will be tracheal intubation.
As the diagram shows, a plastic tube is inserted into the patient's trachea and then a BVM or mechanical respirator is attached to the other end. A source of O2 is also attached. Once intubated, 100% O2 can be supplied to the patient at any volume desired. And once a mechanical ventilator is attached, much finer control of O2 concentration, volume, and other parameters are possible.
Not shown in the diagram is the small balloon on the tube at the end inserted into the trachea. Once the tube is in place, that balloon is inflated, which holds the tube in place and completely seals the trachea from anything entering or leaving except via the tube. In this way, the patient is also protected by the tube from aspirating vomit, blood, broken teeth, or whatever else might be present in the throat.
The OP stated in the comments that he can deflate the reservoir by donning a NRB with a 25 L/min flow of air and then doing strenuous exercises. Specifically:
I put the NRB on and I'm sucking the full bag down in less than half a
breath, after which I'm fighting the safety valve and mask seal to get
Two things explain this. First, he's a healthy person able to do vigorous exercises and then inhale fully to his full lung capacity. Sick people who need supplemental O2 rarely fit that description. In many cases they literally cannot fully fill their lungs with a breath no matter how hard they try, and they are often in distress, which leads to very rapid, shallow respirations.
Second, he was breathing plain air, which is 21% O2. A patient on a NRB will be breathing supplemental O2 at a concentration of about 90%. In other words, every breath the OP took contained 1/5th as much oxygen as the breaths a patient would be taking. I think that if the OP repeated his experiment using 100% O2 instead of plain air, he would get very different results and wouldn't find himself struggling to get enough air.