In the old days, you could study at a library, go to private tutorials, then take a bar exam or accounting exam to become a lawyer or accountant or doctor. I doubt even the public service required a degree, as long as you could pass their entrance exam. There were other requirements for the professions, (such as an apprenticeship), but a degree wasn't always needed. (note, I'm not certain of the details, that's just what some of my relatives have said about how people used to cope without degrees).
The more people get degrees, the more things they are needed for. The lower class were mostly freed by economic growth. In 1960, the UK GDP/capita was about $3 a day, which is about the point where people stop worrying about what they are going to eat, and worry about health, education, their career, and where they are going to eat. If they needed to study at privatized training centres, then pay for a professional board to assess them, they'd have done that too, but the government responded faster than the professional societies.
You're right, and it was the same in the other medieval institution he doesn't talk about-- the Church. Unlike today, you didn't need a Master of Divinity (M.Div) to be offered a job as a pastor or priest. You presented yourself-- and were usually sent-- to a bishop (or consistory or presbytery) as one prepared, usually with Latin and Greek, to "read for Holy Orders." Often, the student was taken into the home of the bishop (!) and ate all meals with his family while being tutored in Greek, Hebrew, biblical exegesis, and Church history. Before the advent of the theological seminary in the early half of the 19th century in America, all ministers were educated this way. It worked very very well up until recently.
I mention this because it parallels the University exactly. They changed the system, and educationally we are all the worse for it because the most important thing now is the credential rather than knowledge. To get the credential you have to go into extreme debt if you happen to be poor. If you don't believe that there's been inflation and the system has gone soft, just take a look at a McGuffey's Sixth Reader. Shakespeare and Dryden at that stage! Something very important has been lost, but most Anglo-Americans don't realise it.
The more people get degrees, the more things they are needed for. The lower class were mostly freed by economic growth. In 1960, the UK GDP/capita was about $3 a day, which is about the point where people stop worrying about what they are going to eat, and worry about health, education, their career, and where they are going to eat. If they needed to study at privatized training centres, then pay for a professional board to assess them, they'd have done that too, but the government responded faster than the professional societies.