I think that all makes sense.

If life was as prevalent in our universe as it is on our planet, I do feel like we would be inundated with transmissions from long dead civilizations. You can't step on grass without also stepping on an entire pocket of bacteria, plants and insect life.

Intelligent life doesn't have to be as rare as a few dozen per galaxy. Even if there were 1,000 or 10,000 world that held/hold civilizations, the galaxy is really big and the window for the radio transmission era (at least hear on Earth) is rather small. So there could be a (relatively) significant amount of sapient life out there, but it'd still be rare to encounter it just due to the scale of the universe.

I'm not sure of interstellar travel is impossible. It probably is by transversal of space. But there could be ways we haven't discovered to travel faster than light, or jump distances without transversal of physical space. Still, even if one other civilization has discovered some kind of teleportation technology, the size of our galaxy is so large they could jump to wolds for hundreds or thousands of our years and never even get close to us. But it's more likely most civilization just goes extinct eventually.