The Guardian (UK) has a fascinating graphic on State of the Union (SOFU) messages. They compared the "reading level" of all of them and conclude that the SOTU has been steadily dumbed down over the years.
James Madison's address would considered the "highest" (25.8) according to the Fleisch-Kincaid readability test. George H.W. Bush's 8.6 measure is the lowest and, therefore, the most "readable." President Obama's recent SOTU was rated at 9.2.
The Guardian's conclusion is that we're all getting dumber. Apparently, we can't understand complex sentences anymore. Incidentally, you may read James Madison's State of the Union address here. It seems "readable" enough.
More likely: From Thomas Jefferson to Woodrow Wilson, the State of the Union was a written document delivered to Congress. (Washington had addressed Congress, but Jefferson considered the practice "too monarchical" and sent a written document instead. Also, Jefferson didn't particularly like public addresses.) Written documents tend to have more complex grammar than do public speeches.
Secondly, in the 20th century, increasing communications capability meant that the State of the Union address would have a much larger audience. Before mass communications, the text would be read by the educated. With mass communication, it could be heard by anyone who wanted to listen.