According to CarAdvice which posted to the question to Tetsuya Tada, Chief Engineer for the 86 and the upcoming Supra, the answer is because it would require a new platform in order for the bosses to be satisfied with it.
"If we come up with a turbo version of the 86 and boost up the power that would result in the necessity of changing the basic configuration completely, to come up with a car I would be satisfied with". He then went on to explain that the weight distribution would be severely affected if the 86/BRZ was turbocharged.
Do you believe this is the real reason or is it more of a marketing move that will allow the Supra to have some breathing space with its superior power output? Let us know in the comment box below!