If the bags on the emergency oxygen masks on commercial airliners don't inflate when oxygen is flowing, why have them?

Humans don't consume oxygen at a constant rate. You breathe in, then exhale. The bags act as a buffer such that the oxygen delivery system doesn't either waste oxygen when you are exhaling or have to have a complex set of regulators to manage inhaling vs. exhaling (like scuba diving equipment).

So, the bag keeps accepting the constant, relatively low volume compared to inhaling, stream of oxygen as you exhale. Upon inhaling, you consume oxygen both directly from the delivery system and from the oxygen in the bag.

Almost all airliners use canisters called oxygen generators that "create" breathable air for each row of seats. It uses a chemical reaction to generate oxygen, which is mixed with the air in the cabin to provide adequate air for each person to breathe for a certain amount of time....up to 15-minutes. Since the system uses air already in the cabin, the canisters are never used when there is smoke, fumes, or fire in the cabin...only when the cabin altitude is too high (above 14,000 feet).

As described above, the bag only handles amounts of air the system generates that is NOT being inhaled by the user. That could happen is you were the only person in your row, and you were breathing calmly during the emergency (cabin depressurized while at high altitude).

The masks automatically deploy whenever the cabin altitude exceeds 14,000', or the pilots activate them from the cockpit as part of an emergency procedure.

The old emergency oxygen system on airliners was a large bottle of oxygen, with lines plumbed to every seat. It was too heavy, and too dangerous.

The bag is not a non-rebreather mask. Therefore, as the previous answer said, you're breathing some oxygen from the mask and some from the surrounding air. A 100% non-rebreather has a bag that completely inflates and flaps that close when you exhale, ensuring that you only breathe in 100% oxygen and don't exhale any carbon dioxide into your air supply.

Non-rebreather masks are frequently used in hospital and/or ambulance settings.