Unexpectedly, Jefferson had an idea for public education, which boiled down to having public elementary schools in all townships, public "high schools" in every county, and a public university on the state level. If this had been carried out in Virginia, and other states had copied it, you could have seen earlier public education throughout the USA. Then you could easily see it carried through to the federal level, with an elite school for "post-graduate studies" in Washington DC.
Jefferson's idea was based on the idea that everyone should get a basic education, and then the state pays for the best 10% to go to the "county schools". The best 10% of those students get a full scholarship for the state university. Carrying this on, the best 10% of graduates of the state universities would be admitted to the elite institution in DC.