I don't think there's any more value in a science degree than any of the degrees you mentioned. University education has always been as much about developing the individual as vocational qualification, if not moreso. By the suggestion that degrees should chiefly be vocation-specific, perhaps we might convert trade apprenticeships into degrees?
It's also the case that an overwhelming majority of jobs are not specific to a single subject. Were the numbers of nonspecific degrees limited, we'd just have a less-rounded workforce, less capable of dealing with real world demands unless they were in their narrow fields of focus for which they had qualified. Lots of degree options = lots of different skills in the talent pool.
"What methods might we use to reduce drug crime on this estate and stop young people becoming alienated?"
"I don't know, but here's a paper explaining why heroin is so addictive."
Essay-based degrees may not prepare you for an exact job, but they do prepare you far better for any other jobs because they involve real-world skills of research, analysis, data extraction, etc. I've always had a bit of an issue with exams in certain subjects for this reason; unless you're required to know your information instantly (I support exams in most science-based subjects for this reason), exam methods offer no value in the workplace because most jobs (especially higher level management, strategy and analysis-based roles, etc) require the kind of thinking that develops via essay-based assessment.
We probably don't need x thousand psychologists, sociologists, historians, etc. But we don't need 20,000 new chemists every year either, and there aren't the jobs for them to go into. Every degree (save perhaps medicine) serves more to educate than to direct someone into a career.
Finally, arts-based degrees already heavily subsidise university spending on science degrees, because a science degree costs several times what an arts degree costs to teach, yet they all cost the same. You'd probably end up with less money for sciences, not more, depending on how government funding was defined.