I tried looking up specific (US) stats on home invasions (as you’re defining it, which I can agree with, vs. burglary) and it seems the FBI doesn’t keep specific stats on that. However, this Atlantic article deals with this topic and that home invasions are rather rare compared to burglaries in general and tend to be overblown as a problem:
I’d guess that the majority of legit home invasions are aimed at specific people that the person invading actually knows? But I don’t know if that’s true or not. I’d also guess that people who get shot by intruders probably surprise the intruder, who didn’t realize someone was home. Again, that’s speculation on my part, but this doesn’t seem to be as major a problem as some make it out to be.