A National University
One proposal that was in many early Annual Messages was that Congress should create a National University in the District of Columbia. George Washington, James Madison, and John Quincy Adams endorsed this idea, but nothing happened. (Locating the University within the District would have satisfied concerns about the constitutional power of Congress to create a university.)
I wonder how higher education in the United States would have been different if Congress had acted. A National University would have wielded a great deal of influence over higher education (you would think) and might have led to a more centralized approach to education more generally. Whether this would have been a good thing is hard to say. One could argue that higher education in the United States is strong precisely because it is not dominated by one or two places (I’m talking to you–Oxford and Cambridge), but critics of our system (especially of its cost) might argue otherwise.