Home invasions happen daily, but the chances of it happening to any given person is very, very low (obviously varies pretty wildly depending on location). If you do happen to catch someone in the act of breaking into your house, the chances that they'll do anything other than try to run is very low--unless you get in their way or make yourself an immediate threat. The chance that they'll stalk around your house looking to kill you (which is the situation you initially described and what I was referring to, but good on you for moving the goalposts and insulting me in the same breath) is insanely low. Does it happen? Of course, it makes headlines and there are podcasts devoted to crimes like that--because it is exceedingly exceptional. You do you if you are mortally terrified of something that will never happen to you and not any of the 10000 other riskier and more dangerous things you never give a second thought to, but just because you're susceptible to cheesy fearmongering on the evening news doesn't mean everyone who isn't is an idiot.
Violence does happen a lot, and it's happened to me a number of times. I've been mugged and had people take swings at me and had far more instances of people spitting in my face screaming and threatening me. Every single one of those situations would have felt and actually been far mor life-threatening if even just I were carrying a gun.
Even an outstandingly tiny number of the scary boogeyman "bad guys" on the news are looking to shoot anyone or get into kill or be killed situations. Even if I walked into my house to find an invader pointing their gun at me there is absolutely no fucking way I'd want to have a gun on me all the way up until they actually fired a shot--and even then it depends heavily on the context.
The chances that 1: someone is breaking into my house at all is super low, 2: they break into my house while I'm inside or I walk in during the act is incredibly low, 3: that person would do anything other than run is super low, 4: that person is even carrying a gun in the first place is relatively low, 5: that person is actively wanting to kill me is absurdly low, 6: I don't immediately just run out of the house myself regardless of their intentions is effectively zero, 6: they've somehow trapped me inside and have fired a shot at me and not seriously injured or killed me and I'm hiding waiting for them to find me so hopefully I can shoot them first is zero because my life isn't fucking The Panic Room.
In high school we had students get killed in drive-bys and by stray bullets from gang shootouts--I bet their families are super upset their kids weren't carrying guns. I bet my friend whose Mom was shot and killed in a dumb bar fight is put at ease because she and and at least a handful of other people were carrying guns. Lol
But as I said, I don't really care either way if you are terrified of the scary stories on TV and movies, and having a gun makes you feel (but usually not actually be) safer. I'll just be over here denying violence happens and voting for the govment to git ur guns or whatever else you think.