I know it's tempting to think about Subaru slapping one of their existing turbo motors in the BRZ but the engine bay of the BRZ is packaged differently from the Impreza and Legacy platforms. It has a lower-profile intake manifold, the throttle is on the front instead of the back, and accessories are mounted differently.
BRZ:
Impreza:
Subaru uses top-mount intercoolers above the boxer engine. In the current-gen WRX you can't see much of what's going on because of the plastic cover:
But the WRX STI uses the older-style 2.5 liter motor and no cover:
The throttle is still on the back of the manifold like all the other Subaru motors and unlike the BRZ.
The BRZ motor is most closely related to the 2.0 NA motor in the base Impreza and the 2.0 turbo in the non-STI WRX. But to get the base WRX motor in there, everything on the base WRX motor is in the wrong spot in relation to the BRZ motor.
That's not to say it couldn't be done, but it would require Subaru to spend the money to properly engineer the turbo motor into the BRZ.