why would the 86 need a turbo? it's a recreation of the original AE86 corolla/sprinter, which was renowned as a lightweight drifting car whose enjoyment in driving comes from cornering and the precise RWD handling rather than power. yeah, stock for stock, it's never going to win any drag races or own any lap time records against other sports cars in its price point (Genesis, Evo X, etc) because that's not what the car was built for, it was built to be an enjoyable, practical, affordable and responsive drive and it does that very well at a $25K MSRP. the 86 is a pure driving car made to maximize precision/handling/feel when driving the car, and it's marketed as such, so I don't see why anyone would even want a turbo in an 86 - power isn't its appeal
and also, the whole "prius tires" thing is a bit of a misconception, the 86/FR-S/BRZ stock tires aren't the same ones that the average everyday stock prius comes with, they're the tires used in the prius' JDM performance plus package. while they're not spectacular, they're not as bad as "prius tires" leads them to be, and most of those who are serious about their cars replace them anyway (as you should on basically any car you're looking to tune)