I would take him
Well, as a player, he's fine. Wins close to 70%. A solid six. He's good for the team in that sense.
If we wanted the best team possible, no matter what, we can just live with it. But we're more about playing with friends and having a fun night out, and it puts a damper on things when one guy is neither serious about league, nor about hanging out with friends, and just seems to want to milk an opportunity for free table time.
I have diff views on this, but if I were a competing team captain I would relieve you of your problem. I'm the capt of a team now and I hate scoring. Fortunately on every team I've had over 15 years there's always been someone on the team that is good at scoring and DOESN'T MIND DOING IT. Doesn't mean they LOVE doing it...just that they really don't mind.
force people to do scoring results in f'ed up scorecards, and team arguments. Your team will have much drama because emotions are transferrable. If you are hot over scoring issues and other tiny issues, the team members will also start to stew about tiny issues. He end result is that your team will self destruct.
My advice, let someone score who likes it. If nobody likes to score, get rid of a non contributing member and replace with someone who wants to learn, and score.
I'd say get over it-I mean that affectionately.

Pool night is supposed to be fun. Let these guys enjoy their time out with the team away from their responsibilities. When pool becomes work, I better be getting paid some serious money for it, cuz I play to enjoy, not to work.
I give my players that same latitude, all I expect is they show up and take it seriously. Sounds like this guy shows and puts up W's almost every time he goes to the table!!! Who wouldn't want him? Don't make the doctor do tedious scheduling secretarial work.
I have a great idea, ...just walk away from scoring, and simply let the scorecard sit unscored...see who starts to score on their own...that's the one most likely to be your score keeper.
I think scoring should be done primarily by one person. They are really used to it and it's not tedious for them. It's no big deal.
The guy you are talking about, is not a numbers guy. It's tedious for him. He hates it. Why put him thru all that?
I've just NEVER heard of a team that had such a problem finding a score keeper...many people like to do it. Ive seen people fight over it, and I've seen captains so insecure that they wouldn't let anyone do it, for fear of losing their power. It's a powerful right. Do a takeaway, tell your team that from now on ...nobody touches the scorecard but you, lol.
are u sure that there's not more going on between you and him...are you just externalizing frustration on him thru score keeping?
Another words, is there more stuff that bugs you about this guy, or JUST SCORE KEEPING?
Just my thoughts,...wow, really makes me appreciate my players who just score, don't complain, and just play, win, and have fun. We have ZERO drama so far, I guess finding the RIGHT people to surround yourself with is equally as important.
Good luck with this guy and your problem, hope you work it out and W I N !!!