Exactly. I like this analogy especially because our needs as a more advanced civilization are drastically different from the function performed by beaver dams. It's not even about energy per se. We could dam all the streams, but that's not a meaningful pursuit given our interests. Likewise, wondering about damming all the stars assumes that solar energy requirements are both the bottleneck and the ultimate purpose of advanced civilizations.
Live in the universe is necessarily finite, because the useable negentropy is finite. It is a plausible assumption that an advanced race would want to keep on living as long as possible. This means managing the negentropy as well as possible, which means dismantling stars and using them. So unless you disagree with my assumption, or add magical energy sources outside of known physics, starlight seems to indicate that there is no race capable of harnessing all available energy.
"We could dam all the streams, but that's not a meaningful pursuit given our interests"
Could you please explain that to the World Bank and governments in Africa, SE Asia, China, and Oceania that insist on damning the last free-flowing rivers on Earth?
Humans dam lots of small streams too for agricultural and recreational uses. They don't get much news, but if you look at aerial surveys of places where people live you will see lots of small dams.