Crazy ideas - higher education tax

There is a strong discussion in Latvia right now on how to evaluate and fund higher education (university education, bachelor degrees and up) in a fair way that has the best advantage to the society as a whole as well as the students and the universities.

On one hand you would want as many people as possible to get best education possible - the lifetime productive output of a person is highly correlated with the amount and quality of education they get. So it is beneficial to the society to just pay for everyone’s education. However, such approach diminishes the quality as both students and universities focus on quantity and forget about quality.

There are many different mechanisms of measuring quality and even trying to force quality on universities (certification programs, mainly) and students (stipends or tuition discounts based on performance), but I have the feeling that all of these approaches focus too much on the performance of the student during the learning process, while the real interest to the society is the performance of the student after graduation.

So here is a crazy idea - give a fully free education to everyone in the country. And to fund it have a 1% payroll (and capital gains) tax for everyone that got a degree under this program, but the twist is that money should be tracked per-person back to the specific university where they got their degree. And that (eventually) would be the only source of government funding for the universities. Thus it will be in the best and direct interest of every university to make sure that every graduate gives as much values as possible to the society over their lifetime, so that the university can take is 1% from that. Interestingly this also encourages the universities to grow some respect for a healthy lifestyle and safety into their students, so they live longer and more productive lives on average :)

There are quite a lot of kinks to work out: What about people who do not graduate? Should government mandate some kind of a basic knowledge level from the graduates to prevent universities just juicing people for their 1%? What to do with master degrees and PhDs? What if those are taken in a different university? Add another percent? What about the transition period? How would new universities enter the market?