^I'm not talking about The End of Eternity itself. In Foundation and Earth, IIRC, Asimov took the idea of Eternity and reworked it, explaining that a time-travel organization similar to Eternity (if not Eternity itself) had worked to create a humans-only galaxy.
It's actually Foundation's Edge
. Dom explains to Trevize and Pelorat on Gaia that they, the Gaians, have a legend, that they don't know is true or not, that a group of humans manipulated time to prevent evolution of sentients on other worlds. If you accept the Second Foundation Trilogy story, then this would be a story created by Olivaw and his followers for the benefit of the Gaians to paint over the original sin of a human-only galaxy. Why look for the truth if you have a perfectly good story that suffices?
A few years later in Robots and Empire
, there's a different explanation given for why only Earth developed complex and intelligent lifeforms -- the presence of the Moon and its gravitation influenced plate techtonics which brought radioactive materials closer to the surface (and thus, closer to life), causing more mutations and, thus, faster evolution. Other habitable planets in the galaxy lacked an Luna-sized moon and they were thus less geologically active.