She's not really a blank slate, either. She can't discuss football or the latest episode of Game of Thrones (yet), but she's always either showing how traumatized she is or showing a desire (sometimes a determination) to be involved in dealing with her case. She comes off as less of a blank slate than him despite not knowing who she is.
The problem as I see it (aside from questions of the actor's range) is that he's supposed to be stoic and married to the job, and that's the wrong approach for a character that Jane Doe needs to bounce off of. Since she's experiencing the world like it's new, her partner should represent the world, someone who actually wants to talk about things that are new to her. Since she's mysterious and her situation is strange, he should be normal, an everyman whose reaction to the situation mirrors the audience's. Since she's traumatized, he should be somewhat optimistic, not afraid to love or whatever his deal is.
Instead, they gave us a bad*** whose bad****** is upstaged right out the gate by hers. His tough guy routine doesn't feel earned because he's an FBI agent in a Special Ops story. It's like trying to make Quentin Lance look awesome when he's in a show with Green Arrow/Deathstroke/etc., just because he can shoot a gun.