I think it is important to understand the USGA's objective with the handicap system. It is not intended to be a measure of relative golfing ability, as such. Here's a link to the handicap manual, a good place to start:
http://www.usga.org/Rule-Books/Handicap-System-Manual/Handicap-Manual/Here are what I think are some key excerpts from Section 1-1, Purpose: "The purpose of the USGA Handicap System is to make the
game of golf more
enjoyable by enabling players of differing abilities to
compete on an equitable basis. . . . the System disregards high scores that bear little relation to the player's
potential ability . . . . A Handicap Index compares a player's scoring ability to the scoring ability of a scratch golfer on a course of standard difficulty. . . . It reflects the player's
potential because it is based upon the best handicap differentials posted for a given number of rounds, ideally the best 10 of the last 20 rounds. . . ." (Emphasis added.)
The two most important words are "compete" and "potential." Take the two players with identical handicaps, say plus 2. Each of the player's 10 best rounds is 70, while player A's remaining 10 are 90, and each of player B's remaining 10 are 75. Looking at the scores, one might say it is clear that player B is a more highly skilled player than player A, so why do they have the same handicaps? Because the USGA's stated purpose of the system is to permit the players to "compete" against each other on an equitable basis, assuming they play to their "potential," or relatively so. For what it's worth, based on their last 20 scores, it does appear to me that player B is a more highly skilled player than player A, but that does not mean A should have a higher handicap than B.
The word's "game" and "enjoyable" are also important to an understanding of the system.
The USGA is protective of the handicap system, so I'm not suggesting someone try this. However, I'd bet that a computer guru could figure how to get into the GHIN system and capture the data in order to construct a different index, say an average of last 25 scores, or whatever the guru thinks the best way to measure relative ability for purposes other than competition on the course, and publish for each player a "skill" index (as distinguished from a handicap index) based on posted scores. Then, in casual conversations about playing golf players could cite both their handicap index and their skill index.