I disagree, I think it's impossible to determine how a home invader is going to react. Most home invasions occur when nobody is home, so chances are if you get caught inside your home by a home invader you've already surprised them and sent them into a reaction. I would argue that many home invaders are going to be high on drugs, in multiple numbers, armed, and already fully aware that what they're doing is dangerous. Furthermore I would argue home invaders specifically avoid homes they know have guns in them, there are definitely ways for a criminal to get this information and we know it's been done before and used in this way.
This is also why training with your firearm is so important. I know not to go searching for an interloper in my house if someone breaks in, though it's easy for me to imagine why someone would under a false pretense of bravado with a gun. If you hear a bump in the night and immediately go charging through your house with your shotgun screaming death threats you are going to be ambushed and killed. If you are sitting behind a locked door using your mattress as cover holding an angle, I can't imagine I've raised my chances of death. Or for that matter being raped.
There is a fixation on home-invasions in the gun community, I do not think they are as big of a contributor as people believe. I'd be far more worried about my roommate murdering me with my own handgun than I would a home-invader killing me in a failed home defense. I think that's more likely and probably far more common, just plain straight up unpremeditated firearm homicide resulting from being close to guns. Difficult to account for something like that. I used to lock away my guns so nobody had quick access to them when I or someone else was under the influence of alcohol, and my routine would prevent someone else from using my firearms against me, but there is ultimately nothing stopping me from murdering someone.
Then again, living in a house with a sword makes you more likely to be killed with a sword, I think that's just the nature of the beast when it comes to lethal self-defense. I can tell you I did not feel any safer when I was unarmed in a high-risk area than when I was armed. I think everyone's situation is different and everyone who wants to own a gun for their own protection needs to evaluate these factors for themselves. In any case, I categorically disagree with the concept of a government telling me how much I need to be worried about my own personal protection.