What does "idea qualitatively about the nature of those [entities]" even mean?
There is a difference between knowing what and who. Knowing what can be done pseudonymously. Knowing who requires guns. Which is it, what or who?
One example would be as I mentioned earlier: How much mining gear is sitting in someone's home-office relative to how much in liquid cooled racks in a datacenter.
I'd also really like to know about jurisdictional distribution of both mining and transfer nodes. I think there are some maps, but such things are fairly easy to fake (and usually fairly dubious even when they are not faked.)
A more ideal system would make some of this stuff more known with higher reliability for operational reasons while preserving as much anonymity as possible. But as I've said before, Bitcoin is what we've got and it's not likely or even possible that it will change in such ways.