I completely hear what you're saying. And you're right in regards to follow up shots and range potential. ARs are much better. However if you are unable to tame a 12g/make accurate shots with a weapon designed for AOE. You should seek firearms training and definitely not an AR.
You can purchase a simple 12g pump for only a few hundred, it's light, easy to maintain, less likely to jam. Has the versatility of a large selection of shot loads. And has the fear factor of being a shot gun. Simply racking a shell is a very effective fuck off.
The thing about recoil, that's only really a problem if you're needing multiple follow up shots. Which 1. Your aim likely sucks. 2. You're a shit person with many enemies and likely deserves it. 3. You're intentionally putting yourself into situations where you'd need an abundance of ammo.
And I've seen those points argued by many firearms instructors while I was researching home defense weapons. But again those aren't the opinions of everyone and we all have our own experiences to base our opinions on. Which is why if I may disagree ever with someone I won't hold it against them. Unless it's just a straight pos opinion like pedophiles should have rights