Formula 1 awarded a point for fastest lap starting with their first world championship season in 1950. The point structure was 8-6-4-3-2 (no points for 6th place) and 1 point for fastest lap. This continued through the 1959 season. So it was a Formula 1 tradition for ten years.
NASCAR was founded in 1948. It is possible that FIA in Paris took the idea of the point for fastest lap from a newly founded regional American race car series, but I kind of doubt it.
In a hypothetical scenario I cannot get used to idea that a driver-X will have 256 points (zero speed laps) earned through his race positions, yet a driver-Y with 250 race points and additional 7 speed lap points will win WDC by a point. Seems absurd.