What can a drunken Robert Byrd really tell us about the American political system? Quite simple. The truth and nothing but the truth. While people like to focus on the president, it is quite clear that the true force in American politics is still Congress and here it is clearly the Senate which plays the overpowering role (due to its only 100 members and need for bipartisan consensus). Thus, Robert Byrd is not far off with this self-description. Big Daddy. The Man.
Senators virtually never lose reelection (the incumbency advantage is even stronger than in the House where incumbents lose seldom enough already). This prominence coupled with the need for a broad consensus (in order to avoid a Filibuster) makes for easy earmarking in the Senate. Ted Stevens (R-Alaska) constructed his famous bridge into nowhere, Robert Byrd (D-West Virginia) assured money for his bio-center. Every senator does this, some more, some less successful.
Drunk politicians really make political scientists' jobs easier sometimes, so thank you Robert Byrd for emphasising this point.