When Steph starts wearing a Batsuit, she becomes their problem though. It's something that is naturally associated with them.
Honestly, I think they were just admitting the truth when they deemed Steph incompetent. In her first appearance, she was caught by her father. In an early issue I have, she nearly gets herself shot when the cops are about to arrest Cluemaster's partners. In the Robin and Wildcat one-shot, Steph jumping the gun allowed some thieves to take a hostage (who luckily happened to be Black Canary). When Tim called her out, she basically said "Screw you, I want Canary as a mentor!"
Granted, the odds were stacked against her as she was kept around as a love interest and foil to show Tim's maturity, but still. Being a crime fighter in Gotham shouldn't be easy and it really lessens the Batclan when all one needs is a spunky attitude and a few gymnastic classes to make it in Gotham.