I keep forgetting that The New 52 has retconned Barbara Eileen Gordon into Barbara-Batgirl's biological mother. In the previous continuity, Babs was Jim's niece whom he and Sarah Essen adopted. Still, the two Barbaras have only been treated as biologically related for the past five years (and, well, implicitly back in the early '80s when Barbara Kean was first introduced in an alternate-universe story), so it's not like it's the only possibility. The show's played fast and loose enough with continuity as it is.
I always had the sense that the weird hybrid nature of this show was the result of the network not trusting the premise. "A gritty crime drama about the corrupt Gotham PD? Who's gonna watch that? Everyone's gonna expect Batman and the Joker and supervillains, so you have to put them in the show! Who cares if it makes sense?" Like how the makers of Star Trek: Enterprise wanted to avoid Klingons and transporters and time travel and all that familiar Trek-universe stuff and focus more on the early days of Earth's interstellar program, but were required by a wary network to stick in more familiar elements for fear that the audience wouldn't be interested without them.
At least Smallville spent its first few seasons avoiding most of the Superman mythos and focusing on stuff that fit its own setting. It didn't start to fold in elements from his adult life and career as Superman until later seasons, and at least it phased them in gradually. Although I suppose the difference is that there's already a lot established about Clark Kent's youth in Smallville that could be used in the series -- Ma and Pa Kent, Lana Lang, Pete Ross, and his early friendship with Lex Luthor from the Silver Age Superboy comics, plus post-Crisis ideas like the teenage Clark discovering his powers and origins for the first time. Not all that much has been established about the first few years after Bruce Wayne was orphaned.
Still, the initial premise of Gotham wasn't that bad. It was supposed to be sort of a cross between Batman: Year One and Gotham Central, a GCPD-centric show about Jim Gordon dealing with the corruption in the GCPD and taking on the powerful mobsters of Gotham City, so you had a lot of characters to draw on like Bullock, Essen, Montoya, Allen, Falcone, Maroni, and Commissioner Loeb. And charting the young Penguin's rise to power in the underworld is not an unreasonable path to take in that setting. And having a background thread of a young Bruce Wayne coping with the murder of his parents wasn't an unreasonable inclusion. Bruce was actually the best thing about the first season.
But they just lost focus. They threw in Riddler and Catwoman and Poison Ivy prematurely, they had Penguin rise too fast and got rid of Falcone and Maroni too fast, they dropped Montoya and Allen for no apparent reason, and it just started to go more and more off the rails and cram in more and more Batman characters, rather than really committing to its early-days characters and threads for several seasons like Smallville did. I never thought I'd be holding up Smallville as a good example of a superhero adaptation, but it did handle the pacing and focus of a prequel far better than Gotham, at least in its early seasons.
Speculations on what Ethel Peabody will someday become after the good Doctor tires of her doubting his ability's?
