If you use the earth as an analogy: why isn't every island on the earth populated with people, since humans are probes, self-replicating beings that communicate with others?

There's a lot of reasons there. Certain areas are unhabitable, or at least annoying to create a habitat (the arctic tundra, for example). Beings may want to cluster together (cities). There may be no interest in going to one territory over another - why bother spreading to all places, where there's so much out there?

Finally, you could have situations in which a probe or a highly advanced civilization could deliberately not contact a lesser-advanced civilizations. How do we know that we're not the less-advanced civilization? See: https://en.wikipedia.org/wiki/Uncontacted_peoples

Not every island is populated by people, but every island is populated with life. Any kind of self replicated probe should take on similar ubiquity.

The thing about B-vN probes is that it just takes one.

I'm not sure how this is a counter to the human analogy? I'm assuming you're assuming probes reproduce and propagate perfectly, but if we assume a 'human reproductive unit' (be it a pregnant individual, a couple, a minimum viable population, whatever) has perfect genetics which can be perfectly replicated, then 'it just takes one' as well. While some sort of b-vn scenario seems plausible, at this point in technological development the practical contingencies of such a scheme are pretty up in the air. I mean, look at it from the other end. If we assume arbitrary technological progress, it's possible probes are everywhere, but we wouldn't even recognize them as technological artifacts if we were starring directly at them.

Both your points assume a lot of knowledge about the future.

They're reasonable extrapolations from current capabilities. Build a self-replicating 3-D printer, make it capable of finding and refining raw materials on asteroids, slap it on a Voyager-like slow interstellar platform, and off you go.

(Yes, I'm being glib, but it's not that much of a stretch.)

Yeah but the energy efficiency required to pull that off? That's not just futuristic, that's astronomically close to violating physical laws...

"reasonable extrapolations" is a far cry from "airtight logical argument". But these discussions rarely seem to go anywhere...