if the gun literally didn't work half the days out of the year, you would be saving 250 lives at the cost of 25, before you count accidents
Though you're (deliberately, of course) not counting the thousands and thousands of cases each year where defensive brandishment stops an attack. That number hugely exceeds the number of deaths by any method. I'd be more than happy to fetch out a handgun in such a situation, but would not be happy to find that it can't ultimately work because I've got gloves on, or my fingertips are dirty, or a battery is low, or it's too cold out, or I forgot my magic bracelet. Or it happens to be my wife's gun, since her's was handier than mine.
I actually very much doubt there are too many cases where you pull a gun on someone defensively and end up not using it in the US. The problem is that in the US too many criminals have guns too, you are not going to pull a gun on someone and tell them to "freeze" unless you are a cop, if you are a civilian in your own home and surprise an intruder you are going to confirm them as an intruder, then fire as soon as possible to ensure they do not have a chance to do the same to you.
Anything else is just a recipe for being shot as the criminal pulls his gun and fires. He knows that anyone he comes across is trouble, since he has already broken in, and is looking at prison time plus the possibility of being lawfully shot. He has so much to lose, he might as well just fire at everything he sees then sort it out later. If you shout anything chances are he will just turn and fire in the direction of the noise on instinct, especially since he may very well have been in that situation before and done the same.
The only advantage you have is that you know your home, you know which floorboards creak and such like and can use that to surprise him. If you do it successfully, you have one, very slim opportunity to get a stopping shot in before he does exactly that to you. Only he will most likely follow up his stopping shot with an execution, followed by the same to anyone else in the residence to make sure no witnesses remain.
The truth is that I am extremely glad I live in a country which has never really let the firearms genie out of the bottle and where there are very few guns in circulation compared to the US. Just being caught with an illegal firearm in this country gets you 5 years in prison, even if it was just a fake and you were pretending it was real. This is a very heavy sentence compared to what you would get for other offences where you could earn a similar financial reward, you could beat someone half to death in their own home and get less time believe it or not.
We have very few cases of the sort of home invasion robbery where a gun would help defend yourself, I guess because most criminals will try and make sure they brake into houses where people are out, or will just run off if they hear people wake up. The only exception to this would be targeting old people since they put up less resistance, and once again, this would get you far less time inside than if you brandished a gun (providing they survived, murder is the exception).