I hadn't really thought of it that way before, but I think you're right, and I think it's a hefty chunk of both Jason's and Steph's Bat-issues. For Jason, he was extra-special-super-mega-desperate for Bruce's attention and approval (in his own way) because he had no one else who had ever given it to him and nowhere to go if Bruce decided he wasn't good enough.
And for Steph, the cowl was always her way of fighting back. Bruce thinks he's saying, "You're not crippled like I am, you have a life; go back to that the way I wish I could." Steph hears, "You don't deserve agency, you don't deserve a way out; go back and accept that you're a victim." So, without either of them meaning it, they fail to understand each other at all.
It's telling that neither Steph nor Jason ever had supporting casts like the one Dick developed, or the one Tim used to have. No family (worth the name), no friends (except other Bats), no team, no future--no wonder they cling to the cowl with all the pure pigheaded Bat-stubbornness they have. And I think that's something which has never quite clicked for brilliant billionaire Bruce Wayne, who always had alternatives.
Which is all me taking a lot of words to say what you said in many fewer, so: motto.