Sounds like you have learned a lot! "I don't ever see happening" bingo.
Many times the reason we stay so hooked in with an alcoholic and are on the merry go round so long is because we don't have a clear reason to break it off things like
He cooks and cleans and helps with the pets, and always goes to work.
That's in your case. We all have our reasons: the physical intimacy, his work ethic, he was there for me 3 years ago when...These reasons unfortunately keep us in an unhealthy relationship that also makes us sick. That ambivalence in itself is damaging.
The fact that your friends have to say things like that says that means it's pretty serious.
There are plenty of guys who go to work, love their pets, do the dishes and don't show up blasted to social functions.
IMO Trust is earned not given. Trust is hard enough without the drinking component.
Given your username on here, if he's also smoking a ton of pot on top of his drinking it can't be a good situation. You seem like a very capable and smart person, you aren't doing him any favors by sticking it out. Sounds like you have a pretty clear picture.
Search the forums, read up and come to your own informed decision whatever that may be.
Welcome!