Why are there not fewer, better funded PhDs? (In the UK)
Universities themselves fund very few students. My faculty (which has 7 departments I can think of off the top of my head, and probably over 250 PhD supervisors) funds 2 students a year. These are used as strategic investments, either in a particular area the faculty wants to expand in, or more often as part of the start up package for a new academic.

So in answer "why not fewer, better funded PhDs", the answer is that any fewer would effectively be none.

In STEM subjects, a large number of PhDs are funded by external funding bodies, such as the government funded research councils. For example my department get 4 or 5 students a year from a Biology and Biotechnology Reserach Council (BBSRC) Doctoral Training Program (DTP). Importantly, government funded PhD studentships are only open to European (soon to be only British) citizens. Then there are CASE studentships that are financed jointly by government and industry. In both these cases the university has no say in how well resourced the studentship is; but they do earn the tuition fees that are paid by these outside agencies.

After our DTP and CASE studentships the most common way for a student to be financed is by a foreign government. These studentships generally are very well resourced because the university can more or less ask for as much as it likes. However payment of the student's stipend is down to that forigen government.

Finally if the student REALLY wants to do a PhD (so they can have a career that requires it one supposes), the university doesn't really care where the money comes from, as long as they get their £18k a year, they are happy and will tell supervisors to supervise them. Depending on the institution and the rank of the supervisor, various levels of compulsion might be applied to encouraging the supervisors to supervise a fee paying student. Supervisors are also often happy to take foreign students because the research funds they bring can see the rest of the a research group through a tough patch.