Re: 1st world problems.
"As soon as the car is slewing sideways more than some 30 degrees from its direction of travel, all four wheels will be skidding and thus leaving marks."
No it doesn't, sometimes yes, sometimes no. Depends on the surface and the rubber used in the tyres and the type of skid. The front tyres are directional and can pivot on the spot. If you do half a handbrake turn and then release the handbrake and roll backwards then the front wheels won't (usually) leave a mark but the back wheels will. Similarly if you send too much power to the back wheels of a rear wheel drive car and spin it, you will often just get rear tyre marks left.
Having worked in motorsport I've seen some very unusual tyre marks left, some of which would suggest a very mutant car if you hadn't seen the spin first hand.