Why is research at highly productive research institutions better than those at not-so-highly productive research institutions?

Your question is a bit circular. The "best" universities are at the top of the list because it's a list of the "best" universities -- however that is defined. :)

What makes a "top" university is largely a rich-get-richer feedback loop: The "best" universities attract the "best" researchers, which makes them the "best" universities. The "best" researchers get the most funding, which helps them do the "best" research. The "best" universities get the most money, which helps them spend more on research.

That explains why older universities tend to have higher rankings. They have had a long time to gradually build up that feedback loop. However, external factors have a big impact -- availability of funding and university management is important, as is the desirability of the location/country. Countries like the UK and US have a lot of good universities because they are attractive places to live and their government provides adequate research funding and, importantly, this has consistently been the case for decades or centuries.

One important point you are missing from your list: Some professors are teaching six courses per year -- they have no time for research. Other professors are only teaching one course per year -- they have plenty of time for research.

An important factor is that "top" universities get more students applying, so they can be more selective about who they admit. Having talented students pushes up standards in general for a university. They are more interesting to teach, so teaching there is more attractive for lecturers, and they ask better questions.

This is a very interesting sort of question. Unsurprisingly, it's surely not the case that people in one region are naturally smarter than those in another. Once we believe that, it is possible to see how the generally-pretty-uniform-brains of people are "steered" in different ways in different cultures.

E.g., in the so-called anglosphere, there is a bit more encouragement to "make progress", as opposed to "adhere to orthodox canons". For those of us in western europe or north america, this principle is completely unsurprising... but, suprisingly (to us here?), this idea is not universal.

In the U.S., for example, in mathematics, the top universities actively try to "collect" the most creative (by a somewhat orthodox criterion) people. Those unis with good endowments can afford to throw lots of money at this goal. There you are.

But, duh, there are many very good people who are not swept up in status-game issues, e.g., if they're more interested in spending their days doing the thing rather than promoting themselves...

Nevertheless, it does tend to be true that the most innovative ideas are most circulating at high-end places. By my observation, this is only distantly connected to funding or status per-se, but, over the long term, does depend on the local status-culture at the place. This can be populist or not, depending. Some math faculties can, as a group, be amazingly Luddite. People are people...

In mathematics, at least, it is not easy to come up with worthwhile new ideas. In the face of bureacratic pressure to "do new stuff all the time", one way out is to "solve problems" endlessly (which ought to be mostly a spin-off of improved technique, but don't tell the admins...)

Then, after filtering out lots of noise, we do sometimes find that the "elite" places have people who have contributed genuinely new ideas (regardless of PR noise about it, and regardless of many other things... whose idiocy does not subtract from the worth of the thing being ridiculously hyped) may be more concentrated in "elite" places. Partly for good reasons, partly for silly. And don't believe the "press releases"? :)

EDIT: under the principle that comments are ephemeral, I wish to add something of @ElizbethHenning's comment and my affirmation, so that these further qualifications will not get lost: to copy my comment on her comment... Yes, indeed, as @ElizabethHenning comments, it does seem to have been that there's a stereotype of what an "outstanding research person" is, and in science, technology, math, engineering that stereotype is traditionally white, male, and with certain mannerisms...

And this does also fit with other remarks about self-referential-ness: a metric can (supposedly) legitimize itself by basically echo-ing the outcomes of other, prior beliefs (whether explicitly in metrics, or otherwise). That is, if a metric does not find the traditionally-top universities at the top, it's not going to be given much credence.

The true effect is that there is _enormous_inertia_ in belief systems, and these belief systems are essentially institutionalized, in the sense that institutions behave as though stereotypes were facts.

The misogyny, sexism, etc, that occur in STEM fields in the U.S. is all the more stunning because many or even most of the people exercising it do not realize that they are, indeed, channeling belief systems that ... if identified explicitly to them... they would mostly find reprehensible, and silly.

It's the old question "what does a mathematician look like?"... We can all fill in the blanks.

Turns out that the "romantic" mythologizing about "killer instinct" and various other pseudo-macho stuff may not have much to do with actual mathematics... but, gosh, then how we would we [sic] prove our macho-ness?

Too large a topic... but/and it does have a significant impact on issues about rankings, status, funding, and so on.