So France is an example where they spend 1.12% of GDP on tertiary education, about 12% more than Germany, and as a result they get a lot more university students, but their labor market overall is less skilled, and French schools -- similar to Italian schools -- are broke and their employees are paid less.
So these are the kinds of trade offs to make -- e.g. what percent of your labor force do you need to have a college degree? This is going to be a characteristic of your economy and providing college degrees to more people than this is going to create a skills mismatch.
A lot of people think the reverse is true -- e.g. that if you train a lot of people to build bridges, then you will have a bridge building economy. But I am of the opinion that knowledge is activity specific, so if you want to have a lot of people who are bridge builders, then you need to actually build bridges, and the university diplomas you need will follow as people scramble to learn how to build bridges to get the good bridge building jobs they see in the economy.
So why does Germany have a more skilled economy even though fewer attend university? Because it's an export monster, that swells the number of high skilled jobs needed to much more than would be the case if they were producing only for their own market.
China is in a similar position -- they want a hundred million engineers, and if that means building a bridge across every river in Africa then that's what they will do. The Belt and Road Initiative is nothing more than an attempt to export infrastructure because they've already covered their own country with empty apartment buildings, unnecessary airports, and so they need to build infrastructure elsewhere. Curiously only 5% of the population attend university in China, and yet they are an economic powerhouse by doing -- and learning by doing -- rather than academic diplomas.
India is an example where they overtrain lots of people in IT relative to domestic demand, and of course what happens is that people emigrate to where the jobs are. Again, you don't transform your economy with university education, anymore than you can transform your car by washing it. You transform your economy by cultivating productive ecosystems and then making sure there is demand for their output.
Whereas we in the US think that we can shut down manufacturing, outsource jobs, and yet have a high skilled economy if everyone goes to university. It's not the case, we have a much lower skilled labor force than Europe and the university graduates have a hard time finding good jobs and repaying their student loans.
So bottom line, the goal should not be to send everyone to college, but to send those people who need to go to college, and if you want more people to need to go, than work on cultivating more high skilled employment in your economy rather than building more universities.