There is mathematical appeal to the argument, but I am not sure about the premise, which is that technological progress would lead to colonizing the galaxy.

I think Vinge was on to something with his zones of thought model, in which the Powers (civilizations that Transcended) removed themselves to a special zone inaccessible to others. Perhaps a really advanced civilization removes itself from the cosmic dangers, leaving planets for Suckers. There are also easily-though-of reasons for Powers to mask their existence (e.g. they might not be interested in meeting unknown Powers with different constitution/utility function).

I'm afraid we are counting white swans as far as the premise is concerned.