The first comment against an STI version of the BRZ is that it would take away sales of the WRX. That is a horrible argument, and here's why:
Brands often offer 2 and 4-door variants on the same basic performance vehicle. BMW, Mercedes and Audi come to mind. Doing so does not reduce sales, it increases them. Why do you think BMW's naming conventions and car lineup is so convoluted and overlapping? So they can please everyone. These cars are sharing the same basic platforms and drivetrains and the more models they can stuff them in, the more they can recoup engineering and tooling costs. As I see it, making the BRZ more desirable by way of more power would drive up sales and help Subaru recoup the costs of creating the platform. The longer a model is on sale and the more it sells the higher the margins of profit become.
The fact that a 4-door car from the same manufacturer exists with a similar performance level won't stop buyers who are looking for the 4-door, and it won't stop buyers that are looking for a 2-door. Example: CTS.
As someone without a family, or the need to have only one vehicle, the STI has always seemed like a compromise: If they could fit the same performance in a smaller package by chucking the back seats and doors, I'd rather have that. People unlike me who want a sports car with some more utility would go with the sedan. Options!