How do you populate a colony? Moving billions is impracticable; giving birth to billions takes hundreds of generations, or then some very severe birth control policies (say, 30 children per mother).
Also, millions of Earth-like planets? Trek has plenty of those, granted, but supposedly only because our heroes choose to visit those rather than non-Earth-like ones. In "Metamorphosis", Kirk exclaims that "we" are on a thousand planets and expanding. Whether that's us the humans or us the Feds, it's orders of magnitude below your estimate. And sort of realistic.