I would argue otherwise because the goal in a home invasion isn't to kill the intruder and leave a big blood stain on the carpet, but rather the get them out of the house with the minimal amount of risk to self and other occupants.

Sun Tzu suggested that the tools for battle should be selected last, after setting the goal and defining criteria for success, then evaluating all the strategies available and picking the one which ticks off all the criteria for success and meeting the goal.

If the goal pursuit and killing of the bad guy? Yes I'd want an AR-15 because of the higher odds of killing the SOB with a single shot. But the reality of crimes against property is that the people committing them have the goal of doing it without getting shot and will nope out when hearing "Get the F out of my house or I will shoot you and not stick around to see what kind of gun you have, or if you actually have one.

If the goal is to escape harm the best strategy — used by organizations like the State Department for its employees and by rich people — is safe haven / shelter in place. Mind you that didn't cross my mind when I bought my first pistol 38 years ago, but back then my goal was killing any SOB who dared to steal my stuff.