I can not disagree more with you on this.
The primary thesis of your original post appears to be universities' shift toward getting people ready for careers that require advanced knowledge (and away from pure learning/research).
That has very little to do with research freedom and the race to publications. Those are both real phenomena, but a) it is arguable whether the former is actually a problem, and b) they are only very loosely connected.
The number of grad students being trained, by contrast, is much more likely to be related to the degree to which universities still value and practice learning for learning's sake—although I think it is somewhat less so than vkou wished to imply, since there are, in fact, plenty of non-academic jobs that do require or prefer a Masters or even a PhD.
My premise is, purely and simply, that you are conflating multiple things that are not the same.
Change everything about the research grant system, and increase funding for it by 10x, and it'll address your concerns, and universities will happily make even more grad students. They aren't currently the bottleneck, because they aren't the sources of research funding - they are just a landlord (with reasonably okay terms) for the research lab that spends that funding.