Another thought to add to the many already pointed out.
When I'm out and about, there's rarely anything around me that I care to protect. Retreat is almost always an option and almost always the best option. And if something does go wrong in public, it's likely someone will see and summon the authorities who are likely to respond rapidly.
At home, I'm surrounded by things and people I want to protect. Retreat is rarely an option and even if it were, it would be a poor one. Worst of all, if something goes wrong in my home and I can't respond to the threat effectively and rapidly, the odds are good no one will notice anything outside or next door. Homes are intended to be private places and they are.
Even if someone does notice something, the police probably won't respond as rapidly because I'm farther from the center of things in my suburban home than in town.
If anything, it makes far more sense to carry at home than it does in public. Maybe the odds are lower that you'll need it at home, but if you do, the need will likely be far more urgent and your options far less varied than in public.