Hi Jaguar,
I'm not sure who alcoholics become when they've recovered, but I suspect most of them do cease being jerks. I recently heard such a story at an Al-Anon speakers meeting. I bet there are plenty more like them.
Your AH has many similarities with my AEXspouse. Mine also displaced his addiction to other obsessive behaviours, in his case, obsessive stamp collecting for a year. The stamps became so important he stopped paying the rent. Sigh.
Mine very rarely became a jerk by saying inappropriate things. Probably because he always drank in secret and was busy hiding his drinking. He would therefore avoid any interactions with me when he'd been drinking.
He's been cycling quickly through relapse and recovery in the past months. While I was with him, he'd have periods of sobriety but was never in recovery. In the last year, he has been much more active in attending AA, working the 12 steps, etc. And when he has been, he really has been becoming the best guy ever. The guy I met but even more thoughtful. When an alcoholic chooses recovery and is actively working his steps, this will include making an inventory of harm they've caused and making amends for those harms. So that usually results not only in not being a jerk in the present but recognizing the jerkiness of the past and, often, apologizing for it. In my limited experience, alcoholics well into their recovery do generally step being jerks.
For what it's worth, I decided to leave my alcoholic, and though I miss the good parts of him, I do believe it was the best choice for me.