I want to start by saying I love the description of yours I quoted above:
An organism must be able to both persist and to adapt. In the long run, it must be stably centred or balanced - hence homeostasis. In the short run, it must be able to adjust that general balance in locally useful ways. — apokrisis
I think that really captures something nicely: I picture the difference between a boulder rolling down a hill at a fallen tree and a deer running down a hill at a fallen tree: the boulder just plows into it, but the deer leaps gracefully over it.
Think of the different ways of drinking water:
1. A towel placed on a spill will "drink" the water, but this is a purely mechanical effect. The towel has no agency here; it's not "doing" anything. Absorbing spills is the
function of the towel, the reason for which it exists, the use to which it is put, and that's one sense in which the word "purpose" is used. But the towel absorbing water is not intentional or purposeful on the part of the towel. And the water is not of benefit to the towel.
2. A deer seeks out water periodically because water is of benefit to the deer. Is this intentional, purposeful behavior? Well, the actions the deer takes to get water might be, might not -- I don't know much about the inner life of deer. Trees send roots into the soil because water is of benefit to trees, and I have no reason to think trees have inner lives. The mechanical process by which roots take up water is probably not much different from the towel's.
3. We drink water much as deer and trees and towels, but we can also choose not to, for any number of reasons. When we do so, we have agency, our action is intentional and purposeful, but it is not our purposefulness that makes water have benefit for us.
One of the things I learned from our last conversation about purpose is that an action can be construed as serving any number of purposes, and that the goals actions serve can also in turn be construed as means for reaching other goals. Purpose is a never-ending hall of mirrors.
What I want to do here with "benefit" is cut that off: water is of benefit to the tree
as a tree, for it to persist, as you said, as a tree, doing whatever it is trees do, whatever it would make sense for trees to think and talk about if they thought and talked. The towel is a particular, but it is not an individual, and so nothing can be of benefit to the towel. Purpose in the sense of function, you can find all over the place; purpose in the other sense, I think only makes sense for us and whatever critters have inner lives enough like ours.
To your specific questions:
But why wouldn't there be a direct connection between purpose and benefit? — apokrisis
Obviously for critters like us there often is, but it's optional.
What would a benefit-less purpose even be? — apokrisis
It should be clear by now that I mostly mean benefit as benefit-to-the-organism whose behavior we're looking at. So I'm happy allowing humans, for instance, to have purposes that do not benefit them. Guy saves a guy at the cost of his own life -- I don't need to concoct some benefit to him to "explain" that. It's just what he chose to do.
What would a benefit be except that it served some purpose? — apokrisis
See that's where I think there's just too much slippage between the senses of "purpose". Water benefits trees, it has a use within a tree, serves a purpose -- but we're just talking functionally here. There's nothing like intentional behavior in the water or in the tree, so I don't see any purpose in that sense.