Divrtim made a great post with many valuable insights. Love them. I am commenting though on it as a means to spend leisure time. But that is what we do here, so let's go...
You can survive without a mask if you don't have ceiling, either real or artificial( extended deco time)
This is very much true of course. An example: I have been deliberatively diving down to -19m or -62ft to the bottom of my local UW playground single without a mask and without fins. I wore a drysuit (a.k.a. a balloon) and I chose NOT to wear fins or a mask on that simple and short test dive. I was an experienced (whatever that means) diver at that time, though. It went just fine. Frog kicks (or any kicks) felt strange though, wearing boots only. It took some getting used to. Also, I could not see a thing... certainly not my depth gauge... as everything was blurred, but as the site was familiar and I could recognize walls and shelves and other larger geological (/industrial) features, I was safe. I knew my approximate depth. I knew my approximate ascent speed (low/ok/too much). No problems. Hence, loosing a mask is not a life threatening crisis, but it does indeed ruin your dive as you cannot see things. If the water is cold though, it hurts. In that case you will need some willpower to maintain a safe ascent rate - or at least to empty your lungs on ascent.
If you DO have a ceiling though, you had better to be properly trained to handle no-mask-situations. All true cave divers and trimix divers are, of course.
If you are doing any overhead dives without the no-mask-capability, then I must remind you of the fact that you really only have one life. Diving without a mask is simple and easy (and annoying) but you have to try it once before your life depends on it, OK?
All this being considered the most likely need for a back up mask is your primary mask getting stepped on on a dive boat. Or, smashed hanging it over the reg yoke, and having it damaged when the bungeed rocking cylinders smash it against the bulkhead of the boat.
Or when you sit or land your tank on it.
You paid for that dive, and it sucks to skip it because of a broken mask.
ps. I am not a native american/english speaker, so if something sounds funny, pardon my French