Sports cars have always made sacrifices in this regard. The first being simply that real sports cars are half the size of a modern saloon, which gives much less room for crumpling.
Err... what? If what you are trying to say, in the most roundabout way possible, is the Tesla accelerates fast- sure. But so does a top fuel dragster, and neither is a sports car.
A sports car is a small, usually two seat, two door automobile designed for spirited performance and nimble handling. Sports cars may be spartan or luxurious but high maneuverability and minimum weight are requisite.
-- Wikipedia
(Notice it doesn't say a damn thing about horsepower)
I think sports cars have a higher power-to-weight ratio typically, but again if this was a prerequisite for a sports car then older cars would lose their sports car status over time.
Alternatively, a cheap car intended to be sporty made by a low-end manufacturer could be disqualified from being a sports car because of higher-end manufacturers throwing off the curve.