That is an innovation that was begun by Ronald Reagan. Dwight Eisenhower, a real general, knew that the salute is for the uniform, and as president he was not wearing one. An exchange of salutes was out of order. (via Greenwald)The State of the Union speech is another ritual that has grown around the Presidency. The constitution mandates a report to Congress, but it does not require the presence of the President. Washington gave the speech himself, but the tradition was discontinued by Jefferson, who believed the practice to be too monarchical. The modern State of the Union speech was reintroduced by Woodrow Wilson.
Of course, no modern President would ever think of forsaking either of these rituals today: they're simply too telegenic.