I figured I'd post this idea on these forums, I'd love to make this myself because it'd be a very easy mod but unfortunately I just don't have the time to learn GTA5 modding.
Back when Rockstar was called Angel Studios, they made a game called Midtown Madness. Not only was it a great game, but it also had an amazing built-in cheat code where you could disable traffic car traction completely. Traffic cars would drive around as normal, but as soon as you touched them or they are involved in an accident, they would lose all traction and skate around endlessly as if on ice. It often resulted in many brutal accidents so it was very entertaining.
Would be legendary if someone can make it happen.