^Everything koko just said.
He's too over-centralizing of a Pokemon because there really isn't a team whether it be stall, balanced, or even hyper offensive that doesn't benefit greatly from having a Pokemon that can switch in on any turn, heal/cure status/ apply status, And provide a new free switch in with Wish.
Does tricking a choice band on him help? Yeah absolutely. It's not infallible. If it was it'd be in Ubers, not UU.
Are there current UU Pokemon that do relatively well against the Pink ball? Sure. Mostly all of them are physical but sure.
The Pokemon still however is in a class better than any other in the tier. There are teams where you don't just stick a Jolly Scarf Moxie Heracross and make it better. But very very few teams get worse with Chansey.
She's incredibly unhealthy for the meta game for these reasons.