[The President] shall from time to time give to Congress information of the State of the Union and recommend to their Consideration such measures as he shall judge necessary and expedient. -- Article II, Section 3 U.S. Constitution
George Washington set the precedent that the president should deliver a speech to both houses of Congress annually, yet history also shows a rich and varied approach to the SOTU -- a time honored tradition that really isn't set into stone.
Of course, the Constitution requires the president to inform Congress of the 'state of the union,' but does not set the timing, how it is done, and/or where or not it is directed to the houses simultaneously.
In many ways, this was a face saving technique employed by Washington. Discouraged by the Congress not gladly supporting his proposals, Washington (and other presidents since) refrained from going to Congress in person to make requests--and yet the SOTU gave Washington a platform to both request his agenda and chide the houses of Congress into action.
For the president, the SOTU quickly became an important part of their policy arsenal, giving them a chance to have an uninterrupted opportunity to make their political case.
John Adams continued Washington's tradition, holding the SOTU annually before both houses.
Jefferson, however, likened "it to a 'speech from the throne' reminiscent of monarchy’s vestiges," and instead opted to send aThis practice continued until 1913, with many SOTU reports exceeding 25,000 words (the size of a small book).
Woodrow Wilson changed this, stunning the power brokers in Washington by restarting the practice of addressing both houses. He used it, successfully, as a political tool to gain support for his agenda and to maintain a semblance of control over congressional policy.
All presidents since Wilson, except Hoover, have delivered at least one address to a joint session of Congress.
Some 20th century presidents chose to occasionally send written reports instead of addressing congress, although Jimmy Carter was the last to do this in 1981.
In a nutshell, there is no real requirement for Congress to invite the president to deliver a joint address--other than the political fallout and finger-pointing that would ensue if they 'dis-invited' the president.
In modern times, with the advancement in media formats, a 'dis-invite' would almost certainly serve to further the president's agenda far more than that of Congress.
In the Washington time-honored tradition of piling your opponents under rhetoric, a long written report might actually serve the president better than an hour-long address. In that way, the president fully outlays the agenda, placing Congress on the rhetorical defensive.
In a sharply divided Congress like today's, a 'dis-invite' would only serve to placate the hardcore party members.Therefore, such a decision would almost certainly alienate and offend many voters; especially those already 'turned-off' by the party antics and power jockeying.
Gaining political points with the base at the expense of alienating the broader, more politically diverse electorate is foolish, but sometimes foolishness still finds itself into political maneuvering.
Image Source: WhiteHouse.gov