The thing is that despite DC's attempt to show Catwoman as THE woman for Batman she hardly ever appeared in the Batman, Detective Comics, Nightwing, Batgirl, Robin, Birds of Prey and such books, and when she did appear in Batman and Detective Comics it was for a short arc where writers would one of two takes with her: the damsel in distress - where she caught herself in a messy situation and so needs Batman's to help her out, or where she was hurt by a villain that is trying to get at Batman through her. Or the wild card thief - where Batman asks her to help him steal something important for him, or infiltrate the villain's business to help him destabilize the villain in the long run. Those are the only two ways writers ever use her. Even then is very sporadic. She's hardly present in any book. Not even in things like Harley Quinn or Suicide Squad she appear. Writers simple don't find her terribly interesting.
There's a big difference between Superman & Lois and Batman & Catwoman.: Lois Lane has always been a fixture of the comics, this even during the times Superman and Lois weren't supposed to be an item like during THE NEW 52. She still showed up regularly in Superman, Action Comics and even Superman/Wonder Woman. Writers like to write about Lois. She always has a place be it in a Clark Kent story or a Superman story.
Catwoman, though, rarely shows up in the Batman comics. I've mentioned this before. She only shows up to play the damsel in distress in an arc meant to showcase their relationship or as an ace in the hole when they need to justify the existence of MacGuffin without much thought put into it and even then she's rarely a presence in either type of stories. Otherwise writers have no idea what to do with her. They'd rather use Alfred, James Gordon, one of the Robins or then one the Batgirls. Not to mention how bloated the Batman cast has become over the years. There's no shortage of character to use. Many much more versatile and interesting to use than Catwoman.