I'd love it if Burnham just kept floating the suggestion that they go looking for her mom at every single command staff meeting just like how Cato the Elder kept quipping "by the way, Carthage must be destroyed," and eventually Saru would learn just simply ignore her whenever she brings it up. Bonus points if Georgiou would try to suggest building their very own empire at every meeting as well.
Saru: "Alright, we finally saved the galaxy - again, I might add. Do you have any ideas on where we should go next?"
Burnham: "We could go look for my mom."
Georgiou: "Everybody has been weakened by these ridiculous crabs and we are the only ship around with a Spore Drive. I'd say the galaxy is ripe for conquest."
Saru: "No ideas at all? Alright, then I shall order the computer to choose a random uncharted planetary system once again. Dismissed."
Except that Cato the Elder finally got his wishes. Carthage has been destroyed to a point that there's nothing left of it.
There's a time patrol story by Poul Anderson named "Delenda!" where someone dickered with the timeline, Carthage was the victorious city and Rome had been destroyed in its place instead. The world was of course completely different. As there isn't a country in the world that hasn't been impacted by the predominance of Rome for several centuries. One detail: the Christian religion in that timeline didn't exist. At some point, the hero asked himself if he had a moral right to change the timeline back and wipe out all the people to serve his own interest. It was an interesting point.