Earlier quoted context omitted.
At the university level, good teaching is a value only some institutions hold. They'll all say they care, but research schools are paying way more attention to grants, publications, parents, etc than to student evals. There are universities that prioritize teaching over research and, unsurprisingly, they tend to have better teaching professors. I went to a school that didn't emphasize research and never had a TA teac…
How much research do we need? Sure there are advances to make in physics, but do we really need another paper explaining why Richard III wasn't completely evil, or whatever similar activity English professors research? How much more research into the real nature of the Greeks do we need? Don't get me wrong, both are interesting subjects, and the thinking that goes into those papers is worth teaching/knowing. However…
For example, the fields you mention (sciences/engineering, medicine) pull in vastly more money that humanities. Because they have more money, they hire more faculty, and they also train and graduate more PhD students.
I knew a few humanities PhD students while I was in grad school, and none of them were funded by research grants. If they were lucky, they got fellowships. That's a stark contrast to engineering where both grant and fellowship funding was relatively plentiful (though I've got a few horror stories there too).
On top of it, humanities jobs are really hard to find (even more difficult than fields like physics that are already known for multiple postdocs, etc.), making it a bad deal all around for PhD students in those fields.
Overall, I think things are already allocated more or less the way you expect, and I don't think we need to piss on humanities for this. They already have it hard enough.