Actually, I think HA can really help here. I was the unfortunate recipient of a guest to my home who visited while I was away. Turns out I forgot to provide a key, so they found an unlocked door in the back. I never unlocked it, but the door jam shifted and allowed them to come in. I guess I was away too long because they decided to leave before I got home. If I had better HA, I would have made sure that the front door auto-closer was active so when they forgot to shut the door, it would have closed and locked itself. I would have preferred the 2 back doors had a similar mechanism installed so I'll add that to the to-do list. Since the issue was caused by not having remotely controllable dead bolts, that can be added to the list. I do think a Roomba would have been nice at the time since my guests forgot to take their boots off and they tracked dirt around the house. Perhaps something on my thermostat linked to the doors so it would know that the doors were open and not to kick the heat on full blast in January.
Actually, I think the best HA device that would be applicable here would have been what the responding officer explicitly said to NOT install. I think a sentry type shotgun mounted near the entry door would be cool. I've seen some testing performed with paintball guns that looks very promising. The videos are a few years old now, so I imagine a shotgun or AR could be incorporated. This would be great coupled with a Ring brand doorbell camera so you could politely request that the
zombie corona-carrier respectfully leave the premises. In movies they always have to cock the pump action shotgun prior to discharging so maybe that can be done with an audio element since you don't want to warn someone by dropping and wasting a round onto the ground.
I'll keep thinking about this and see what else I can come up with. This is a great idea!