I think you're both right.
The whole point of Tim becoming Robin was because other people needed that role filled.
But Tim was, very early on, a bigger character than just that role.
And while the original role that brought Tim to the Robin costume is no longer viable, that doesn't mean Tim himself isn't viable. If we hold Tim to that original role and narrative purpose, and refuse to let him grow or evolve, then we must also complain about Dick growing up, becoming Nightwing, and forging a life for himself away from Bruce.
Tim can still have a purpose and role in the Cave, it just can't be what it was twenty years ago. The only problem right now is that DC hasn't figured out what that role is yet. But that's something that'll come in time.