ELI5
 

Why don't street cars have horizontally mounted dampers like race cars do ?

Cost.

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I'm going to pretend your a teenager:
Because it's unnecessary and would be difficult for minimal gains.

First examine why racecar dampers are placed inboard: Aero
Moving a tube the size of a drinking glass out of the airflow makes a big difference when you're spending time up over 150mph, but with modern street car bodywork you would see almost no aerodynamic gains so the primary benefit is eliminated. There are secondary effects about moving mass inboard and potentially reducing unsprung weight but we're talking about production cars, unsprung mass isn't going to get you through traffic better or help your Prius get 51mpg instead of 50.

Now the hardship, where would you locate the dampers? Looking at the 86 I honestly don't know what you could do with the dampers that's more space efficient than where they currently are, behind the wheel. Mounting them horizontally means they have to be before or after the axle in order to translate the motion effectively without loss, again no idea how that would fit up front. Maybe in the rear you could reduce the wheel well size and place them kind of where the spare tire sits, then you shift everything around back there and lose a bit of trunk space for a very minimal gain. Also consider that this kind of suspsension setup basically necessitates a double-wishbone/multi-link control arm setup, in the 86 and many economy cars that would necessitate the addition of suspension mounting points up front in an extremely tight area, added mass, parts cost and complexity, and reduced space for working on the car.

tl;dr imo the pro's don't outweigh the con's for consumer vehicles.

Because it is a street car and not a race car.

Race cars are usually not subject to things like budget, comfort, reliability, cost of production, etc.

-alex