Considering Supergirl's got all the same superpowers and can do pretty much all the same cool things on screen, I don't think people will really miss Superman or feel his absence nearly as much as Batman's in BoP back in the day.
Well,
Birds of Prey had many flaws, but a failure to justify Batman's absence was not one of them. It established right up front that Batman had been broken by the Joker's murder of Catwoman and paralyzing of Batgirl, that he'd retired from crimefighting and left Gotham. It's hardly flattering to Batman, but it was a clear and consistent explanation for his absence. There was a lot about the show that made far less sense than that. (And it has a parallel in Nolan-Bruce's 8-year retirement between his second and third films.)
The only issue I can see is if they have her continually going up against huge, massive threats and Superman never shows up to help. Since surely he can't be busy with something else every time, or wouldn't just show up in the city to help at random times anyway.
Well, that's no worse than what we already deal with in shared comics universes. I often wonder, if Metropolis and Gotham are so close to each other in DC geography, how come Superman can't swoop in and clean up Gotham on his lunch hour? To some extent, you just have to suspend disbelief about such things.
(In my Spider-Man novel, I included a conversation where Peter explained to Mary Jane why he was generally the "first responder" for mid-level supercrime in New York City, because the Avengers tended to deal with bigger, more global threats, the Fantastic Four focused on superscience crises, Doctor Strange dealt with the mystical, and Daredevil tended to limit his activities to Hell's Kitchen. Although I probably overlooked characters like Luke Cage and Iron Fist. And it's still kind of a fudge. I actually did include references to other heroes dealing with side effects of the novel's crisis "off-camera.")
Anyway, the fact that this is on a TV budget probably limits the number of "huge, massive threats" we'll be seeing. A CBS show may have more money to spend than a CW show, but it's still nowhere near a feature budget. So we probably won't see that many crises that require two Kryptonians to handle.
