Getting rid of all the stars in one part of space and replacing them with near CMB doesn't seem to produce what we see: it would produce a raised CMB signal in one direction (would it be strong enough to pick out? How close, exactly, to CMB would it be?), a reduced star density in one region, and presumably a bunch of half-eaten galaxies on the boundary of the region.
The point that "it would be an amazing coincidence if alien engineering just happened to look exactly the same as pristine nature" seems reasonable convincing to me.
I think the idea is not all the stars in a region -- it's one star per civilization. The basic idea is to maximally exploit energy transfer between the star and interstellar space, so optimal efficiency makes the artifact appear from the outside to be as close to interstellar space as possible.
An uplifting message as we enter the new year, quoted from Edge.org:
A few thoughts: when considering the heavy skepticism that the singularity hypothesis receives, it is important to remember that there is a much weaker hypothesis, highlighted here by Tegmark, that still has extremely counter-intuitive implications about our place in spacetime; one might call it the bottleneck hypothesis - the hypothesis that 21st century humanity occupies a pivotal place in the evolution of the universe, simply because we may well be a part of the small space/time window during which it is decided whether earth-originating life will colonize the universe or not.
The bottleneck hypothesis is weaker than the singularity hypothesis - we can be at the bottleneck even if smarter-than-human AI is impossible or extremely impractical, but if smarter-than-human AI is possible and reasonably practical, then we are surely at the bottleneck of the universe. The bottleneck hypothesis is based upon less controversial science than the singularity hypothesis, and is robust to different assumptions about what is feasible in an engineering sense (AI/no AI, ems/no ems, nuclear rockets/generation ships/cryonics advances, etc) so might be accepted by a larger number of people.
Related is Hanson's "Dream Time" idea.