Accountability confers enormous power. White House advisers may fight battles in their memoirs, but only the President is held accountable for presidential actions. Presidents also tend to be held accountable, at least by the political opposition, for actions of distant subordinates. [See Benghazi and Cincinnati IRS office for the latest examples.]
Fred Kaplan has a fine piece listing several important presidential decisions against the advice of his national security advisers, including Kennedy during the Cuban missile crisis, Reagan on "star wars," and G.W. Bush on the 2007 "surge" in Iraq. Obama's reluctance to get more deeply involved in Syria is just the latest example.