I'm mostly in agreement with what Tate said. However, I think the tighter pockets only benefit the higher level players.
Here's my reasoning. At my local pool hall, I constantly see people fighting over practice and play time on the tight pocketed table in the room. All citing it improves their game. Nothing wrong with that. But I just don't believe it is NECESSARY for the improvement of most players. Particularly lower skilled players. Why? Because lower players don't even hit the pocket on buckets often enough. As a result, the smaller pockets aren't justified.
It isn't as though they are making shots with such boring regularity on the buckets that such bucket pockets are now obsolete in exposing their stroke flaws and aiming error. I see people who are APA 4's want the tight pockets for the challenge. I always think to myself: for them, buckets are still plenty of a challenge. It's like golf. If you can't get par on a par 3 course, you won't up your game playing on the toughest PGA courses in the country.
I figure it like this, if you aren't up around 95% or better (preferably better) on a particular drill or shot on buckets, then the tight pockets aren't going to be a significant help. You can achieve excellence on buckets - just up the standard. 50/50 isn't good enough to "graduate" to the challenge of smaller pockets.
Where tight pockets matter is when you can make a particular shot nearly every time on buckets. The tight pockets will force you to be even more precise after you've already improved your accuracy to the margin of error of buckets. Buckets for beginners to lower skilled players might actually be better, since at least the 5" (give or take) target at least gives back feedback as to whether they hit it or not. On a table like a Diamond, most of these players do not pay close attention as to where the ball hit when they missed. Was it off the point? Was it 1/2" off the point? That tends to be overlooked. And that might be an argument in favor of buckets for beginners. More feedback. That's a major deficiency among beginners or lower skilled players. They don't remember what they did or what happened. Or they have less awareness. Often, many aspects of the game are so challenging for them that they are putting everything they got into making a shot and keeping their body still and stroke straight that they have little awareness.
Lower players missing on tight pockets is no different than missing on buckets most of the time. They usually miss by enough to have missed on either. Yes, the tight pocket will reject shots that would have gone on the buckets, but how helpful is that? Given the wide range of inaccuracy a player has at that given point in their game.
There are many types of flaws in a stroke. Some players have incredible laser accuracy most shots but when their stroke breaks down or that flaw appears, the miss is no where near the pocket. Tight pockets won't matter for them. If they are more advanced, that flaw that rarely appears might be within the margin of error on buckets, but not on tight pockets. For them, the tight pockets are of good use for improving their game.
For lower skilled players, what's going to improve their game has little to do with how small the target it, and a whole lot more with them taking more of an active learning approach to improving fundamentals such as stance, stroke and all that good stuff. What's going to make them hit the buckets with regularity will also have them hitting the tight pockets with regularity, just not as much. In other words, the tight pockets are good for tweaking one's game and squeezing one toward higher care, precision, focus and accuracy.
That extra difficulty requiring better accuracy and all that don't help someone who isn't very, very consistent on buckets.