I agree that a lot more needs to be done to actually have this discussion. First, a correlation has not been established by the OP. Thus far there has just been select examples on both sides, which is not analysis.
1. Is there a correlation? Not yet known in this thread.
2. If a correlation is established, correlation is not necessarily causation; see discussion below.
3. We also dont have a consistent proposal: is it absolute arm length? Is it wingspan to height ratio?
There is a way to address this question. Barring obtaining data for the entire NBA, One easier way to do this would be to take a random sample, say 2-3 draft classes. Remove players who didnt make the nba. Make a spreadsheet with the columns of name, wingspan, wingspan:height ratio, career TS%, career 3pt %, career ft%. Then plot the various shooting stats vs height and vs ratio, and see if there is any correlation.
Now, even if a correlation or association is there, it does not mean causation. I believe even if there was a correlation, there is a very plausible explanation. Basketball is a complex game, and there are many different ways to have an NBA career. First, basketball consists of offense and defense. In general, long arms help with defense. Since quickness is more associated with weight and height, on defense, in order to guard someone, you typically have to be about the same size. However, if you possess relatively long arms, you will effectively be a better one on one defender, and a better rebounder relative to your position. In terms of absolute wingspan, you are more likely to be able to contribute with help defense, reaching into passing lanes, blocked shots, and rebounds the greater you absolute wingspan is. Now, offense isnt just shooting, either. A big part is passing, where longer relative arms may help with angles and avoiding defensive arms. I dont know how wingspan correlates to dribbling. Finishing at the rim is a huge part of offense though, and that seems intuitive how wingspan (both absolute and relative) can help you finish at the rim against the players typically guarding you.
Because very few NBA players are good at all skills, there are many ways to construct a team using many imperfect players, but you need to make a team that can play offense and defense.
So it may not be that longet arms MAKE you a bad shooter. It may be that long armed shooters are stars. Then you need to fill in the gaps. You might then find a guy who is a great shooter but bad at defense, bad at defense because of short arms. It is not that the short arms make him a good shooter, its that lack of long arms prevents him from being a star. Then, to help you team be all around better, you go looking for good defenders. All these guys who are goodscorers and defenders are highly paid on other rosters. So you find some flawed guys, guys who are NBA caliber because of there defense, and they are good at defense because of long arms and happen to lack the skills to shoot.
Then, what we dont see, is all the NON-nba players, who lack the skill to shoot AND cant make up for it with defense and rebounding because they also have short arms. There are tons of those out there.