First of all SORRY THIS TOOK A DAY OR TWO i wrote half of this response and then forgot to finish wksjsj
I do think batcat is a more realistic ship for batman in general! There's so many good reasons why bat and cat work well together (similar motivations, arguably similar priorities in that they both to their bones feel Gotham is their home and want to make it better, similar moral codes (despite her being a thief), etc.) even if the some of the recent batcat comics haven't been... great characterization wise (Tom King my beloathed)
My issue comes from kinda like with when people make Spidey pool aus with their blorbos, esp since the 2022 Batman movie came out I've been seeing a lot of batcat aus with people's blorbos and idk, some of it doesn't sit right!
Part of it I think is that so often people replace Catwoman with a white dude and while Catwoman isn't always a woman of color, she definitely is in the movie they are pulling from so that always feels a little sketchy to me. Some of it is that people obviously don't really know Selina outside of Bruce which can also make any blorbo adaption of them feel weird. Which is sad because Selina is awesome!
Selina is an amazing foil to Bruce, but also really dang cool on her own whether she is wrangling the Gotham organized crime scene like she has in recent comics, or simply taking young sex workers under her wing and giving them a place to get on their feet like she was often seen doing in the New Earth era!
(Honestly, even when she is just being a more "shallow" villain and just stealing cat themed items from museums and also having psychic connections to her cats is fun too.)
Controversial opinion, but I think people just get to stuck on trying to fit their blorbos into preconceived boxes based on comic power couples, and that superhero aus would be way more fun if they utilized lesser known ships, or learned the truth that comic book fans know, which is that at any time your fave could suddenly be in a whirlwind romance with a teammate or random other cape. Match up your blorbos with a character that actually fits them and shipping will come later ;P
(Sorry I am still a little wonky in the head rn from being sick so if this doesn't make complete sense.... oops.)