They asked Bob Kane to make a superhero like Superman because he was printing money. He asked "how much is that worth to you" and when they gave him a figure, he replied "you'll have a superhero by Monday."
He then made his infamous red Batman and then Bill Finger made the character we love today which Bob promptly stole credit for. He is 100% a response to Superman. At least learn your stuff before trying to downplay history to fit your narrative. You're making it very clear that you don't actually know what you're talking about. Yes, the inspiration for the assignment was more inspired by pulp heroes, but the visual was retooled to be entirely based on Superman (who himself is riffing on strongmen of the era), but the assignment itself is a response to Superman. You are categorically wrong. Without Superman to create the big bang, so to speak, Batman doesn't exist. It's simple cause and effect.