You are missing the point. A pistol is sufficient for ‘home defense’ if we are talking one or two ill-prepared intruders. For defense against someone or some group intent on doing you or your family harm, and potentially equipped to do so, a pistol is a backup option.
Pray to god that you never need to be in a fairly lengthy fire fight, especially at or near home! But if that ends up being the case, you will want a rifle with the capability to throw lots of lead, quickly, and for a sustained period of time. AR is the cheapest and debatably best option for the most part. I have put together functional and very reliable ARs for under 500, but I am in NH. In MA, that same rifle will cost you about 3x the price if you can find one willing to be sold. They do get much fancier.