How did Asimov paint himself into a corner? It seems clear that by the end of Foundation and Earth, Asimov had become interested in the idea that even if Galaxia were established, it could come into conflict with aliens from another galaxy. However, Asimov never had much interest in writing about aliens, so I suspect he could not take seriously the task of inventing an alien creature from "a galaxy far far away" that could be bothered to challenge Galaxia for control of the Milky Way.
If we take seriously the "hint" from Foundation's Edge that Earth robots established Eternity and used Eternity as a tool to "select" a Reality in which humans alone spread and dominate the worlds of our galaxy, then we can easily find a way to get Asimov out of the corner he had painted himself into. If
1) telepathic robots with positronic brains discovered time travel
2) there are alien species with human-like intelligence in other galaxies
then we have to ask: why can't more than one species discover time travel? How can it be that robots from Earth are the only ones to travel in time?
I don't think it makes sense to assume that robots from Earth are the only ones who can travel in time, but I have no interest in getting involved in some sort of "time travel war" as depicted in Star Trek. The "Exodemic fictional universe" provides a way to allow aliens to engage in time travel while not ending up in a seemingly inevitable "time travel war".
The first step out of Asimov's corner is to assume that positronic brains are a freakish invention of humans. Many aliens make robots, but they all use electronics when they make artificial life forms...except for humans. It must be explained in The Start of Eternity why humans were silly enough to develop positronics and why that allowed for the development of telepathic robots and time travel.
The second step out of Asimov's corner is to assume that there are aliens in other galaxies who have been around for hundreds of millions of years. When they discover that robots from Earth have telepathy and time travel, the aliens are disgusted with the implications and they do not hesitate to engineer a Reality Change that will rid the universe of these abominable telepathic robots and their creation: Galaxia.
It is not surprising that Asimov could not take these steps out of the corner since he had invested so much in his vision in a fictional universe culminating in Galaxia. However, I think painting that corner in this way (The Start of Eternity) is a way of honoring Asimov's imagination and his "Robots and Empire" fictional universe, even if Asimov was not able to take the story in this direction.