Eh, I've said it a dozen times I'm sure. They best ideas come in community. I may have come up with Haly's Casino, but I only thought of it in the framework of the triple life that you introduced.
It wouldn't be a massive benefit, but the brand recognition might be good. Though, it also has its own history as "Batman's team." A fresh start might be better.
There are also definitely strengths to having a sidekick be a brand new character coming from Dick's world rather than a preexisting Bat or Super. Dick not needing to borrow big names in order for them to stick would speak to him being an A lister.