You ask a good question. I can't point to any study but I did spend a couple years of roughly twenty hours a week on a snooker table. It was an antique of unknown vintage and viciously tight. A shot down the rail could only be made with helping english. Even that wasn't quite true because the english needed off the inside rail would reverse with a different speed. A long bank had to have at least a half table between the legs. As might be expected I got pretty decent on that table and was soon playing shape about as well as on a pool table.
My game got better, but it also changed. Took me awhile to realize that. Because I would shoot the reds and wear out the seven ball I was playing on very tight pockets but I was also spending seventy-five percent or more of my time playing on a 3'x6' area. Then the final six balls were basically a drill, mostly shot them the same every game.
The snooker table was more like a bar table than a nine footer and it did more for my bar table game than my big track game. It also changed my shot selection and choice of when to shoot and when to play safe. In some ways it helped my game, in some ways it hurt it. Once I realized that I could make corrections and I was still playing many hours a week on the tables I was gambling on.
My opinion, tight pockets can harm your game if that is all you play on. If you continue to play a lot on both it has less effect. If somebody is going to spend a huge percentage of their time on their practice table I think they may be better served with the same pockets they gamble or shoot tournaments on. For a fifty-fifty mix or similar tighter pockets can improve some areas of play.
I got a chance to play with an 11.8 CF shaft. It was a REVO but not exactly. A larger shaft had been ordered, the 11.8 came, well before it was released for sale. I don't know if it was a prototype or what. I had been struggling on a snooker table with a 13mm shaft or a touch bigger. I shot a few balls with that REVO and they found the pockets like they were on rails!
Without a lot of data to work with this is more opinion than study of course, everything in this post. I would say that tight pockets can improve both pocketing and position play, all shooting skills. At the same time they can mess up other parts of your game. I think if I bought a home table it would be a coin flip if I was trying to improve my game. For pleasure I would prefer a ten foot table, preferably snooker table.
Not a study but having worked in research and development I have never seen a pool related study that I thought reached the level of scientific method required to try to put great weight to the study. More like experiments that might indicate a direction for a study to go.
I hope this provided food for thought. I can't say it is worth more.
Hu