The least common way of a burglary happening is someone picking a lock.

You don’t need a gun to defend against a burglar. Burglars are generally cowards and run away when caught. The whole point of sneaking into your house is to not be detected and commit theft. (taking something without a person noticing it).

What you might need protection from is robbery (taking things under thread of violence). A robber is not going to sneak into your house. They will either kick down your door while you sleep or simply ring the doorbell and wait for you to open. Do you bring your gun every time someone is at the door?

They specifically said they think it’s true that carrying it most of the time isn’t the point.

Then there is no point. They will just wait until you are not carrying to rob you.