When seconds matter Police are just minutes away.
So is a gun, unless you keep it loaded in your pants 24/7 and take it into the shower and sleep with it.
No gun is going to save you from someone shooting you from behind without warning.
If you are a victim of a burglary, would you rather have a gun in your house, or a telephone in your house?
To JJA's point, one would mostly likely need some element of surprise in order to gather a gun, possibly have to load it, then confront said burglar. As well, it's a complicated legal issue as to whether you can take up arms if the situation is questionable regarding personal safety.
Some States in the US will send you to jail if you shoot a burglar if the burglar has not threatened you in-kind. About half the States.
Even in these "Stand Your Ground" States, they have certain restrictions when it comes to using force in self-defense.
For example, they may require that the threat of perceived harm is objectively reasonable and that the force used be proportional to the threat. Stand your ground laws may also require that the person using self-defense be at the location lawfully (no trespassing, for example) and not be the initial aggressor in the altercation.There are some nuances to the laws as some apply to the home. Some apply to a place of business. Few apply to public space. Some apply to only when a felony is being committed, etc.
I'd definitely call 911 with the phone that's always within reach first before I'd go rummaging for my gun.