It’s more capitalism than government desire, I’m afraid. Before the push for higher numbers of kids in tertiary education, how did many of the non-university educated kids get jobs, pre-Thatcher? Employers took them on and trained them. A young person might not have been productive to a company for years; but near full male employment and union power (and few women in the workforce), all meant that if companies wanted to employ more workers, they largely hadn’t much choice other than to take on young people and train them up, either informally or through formal apprenticeships and vocational qualifications.
Post 1980s, that all gradually melted away. Employers now want ready-trained young people: they don’t want to pay to train them.
In-workplace training schemes these days are like unicorns. Employers found it much more pleasant to employ workers on temporary and insecure contracts than to take on school leavers and invest in training them.
The early Blair governments tried a lot of finances and structural incentives to get businesses to invest in training: they simply wouldn’t. I heard CEOs at companies and in focus groups just saying things like “I don’t want to pay to train my workforce”. Lots of the push for re-establishing technical and vocational schemes in the very early 2000s crashed and burned because despite interest from young people, employers and businesses just wouldn’t get on board. They want individuals to take on the debt to train themselves up at universities and colleges, and then just employ them all ready skilled. Cheaper and convenient and doesn’t require any long term commitment to the workforce.
On another note, it was also always a myth that (say) boomer age cohorts didn’t have large numbers with tertiary education. A very large proportion of those cohorts did study at tertiary institutions, including polytechnics, FE colleges, teacher training colleges, and so on. Obviously after 1992 many of those institutions became universities: but if you look at pre-1992 cohorts and add university cohorts to those who went to pre-92 FE institutions, you get a much clearer picture which is that those generations always did have a lot of exposure to tertiary education and training as well.
On the degree subjects - disciplines like nursing are not at all like they used to be decades ago. Many functions nurses used to perform are done now by healthcare assistants. Nursing has been a very high skill job for a long time now, with a lot of complex elements. Nurse practitioners and nurses in high-tech specialisms like ICU or chemo delivery are extremely highly skilled and require degree-level training, including in the mathematics required to calculate drug delivery and operate very complex technical machinery. I have a close friend who is a nurse and has a PhD in ICU nursing practice. Many nurses in joint practice/research roles carry out research projects at universities.
Nursing is a discipline that is rightly degree-level these days, and ought to be paid a lot more. Healthcare assistants too ought to be better trained and paid IMO as well.