It doesn't really do that, because it doesn't subtract out offensive rebounds -- ie, the offense is not limited to only one FGA per possession. It is fair estimate of number of "Plays." But that's beside the point. Even as a fair estimate of % of "Plays" that end with a player...I still don't see what this stat is trying to achieve. So what if it tells you who ends a play. What is the big value in that? We already have many other stats to talk about the players who end the plays. I don't get it. Seems like a made-up stat that adds little value to our existing stats.
If we can agree that there is value in knowing the percentage of a team's field goal attempts for a player when is on the floor, then by extension there should also be value in knowing the percentage of a team's shots attempts + turnovers for a player when he is on the floor. It provides a context for better evaluating the player's efficiency. Instead of as a measure of how much the ball is in that player's hands, think of it more as a way of capturing how much the team relies on him to score the ball.
I would agree that Usg% is a weird stat in that, by itself, doesn't really measure anything of importance. As others have said, it's an estimate of how much of a team's office goes through that one person. The key word there is estimate. Not sure why BR wouldn't include assists as it would be a logical thing to include considering assists is part of the offense. Also not sure why Hollinger adjusts for pace since this should be a percent stat based on team minutes and not a rate stat that is relative to league average since teams play difference offenses. Anyway, can this stat be useful? Again, not by itself. You also need to look at efficiency stats, like PER and eFG% or TS%. Then you can (kinda) see if a player is being under or over-utilize. I say kinda because Usg% is an estimate and same for PER. Plus there's obvious disagreements about how to best express the actual formula. Perhaps I'll include Usg% in my GameScore analysis so you can maybe see if Mchale did a good job of figuring out who should have gotten minutes in a particular game.
Just think of an offensive rebound as a new possession, although I realize that's kind of contrived lol... anyway, I would agree that the usefulness of the stat is subjective. I think it's useful to see what percentage of a team's "possessions" or "plays" end with that player when he's on the court. I can see why you might think that kind of thing is useless though because there are plenty of other stats that cover the same area.