Not sidekicks in general but Batman's having a child
He's going out there and fighting armed thugs, murderous maniacs and people bent on destroying Gotham and as an aide Batman brings a twelve year old boy
in hot pants to help?
It doesn't really fit or make sense.
Robin as a sidekick is very, very different than Holmes having with him an intellectual near-equal, adult, doctor.
As for other child or child-like sidekicks, I don't think they fit well either. Jimmy Olson was a tool and probably more annoying to Superman than as a helpful "sidekick." And the idea of putting a child into a movie to give child-readers someone to connect with is the type of stupid thinking that gets us Short Round and a young child Darth Vader.
When kids read these stories or watch these movies they don't want to be a child hanging out with the superhero or the hero they want to BE the hero. It wasn't "Gosh! I wish I could hang out with Batman in a pair of pantyhose and help him kick the ass of murderous thugs while mostly being ineffectual and end up getting caught to give Batman more of motive to do his self-appointed job!" it was "Man! I wish I could be Batman and an unstoppable bad ass kicking the ass of murderous thugs!"
A late teens or 20-something Robin would make a touch more sense and being more acceptable, but a child is just an idea that I think has gotten harder and harder to swallow over time.