On an all-wheel-drive car both axles are linked through the transmission, so dragging it with two tyres on the tarmac turns parts that are not meant to move with the engine off. Toyota's RAV4 handbook says AWD versions must travel with all four wheels raised or the drivetrain may be damaged, and Subaru calls a flatbed the only recommended way to move its AWD models.
Two-wheel-drive cars have a little more flexibility, since the same Toyota guidance accepts raising just the front wheels on a front-driven model. Many automatic gearboxes are not built to spin for long with the engine off, so handbooks often rule out towing with the driven wheels down or set tight speed and distance limits.
Electric cars add another reason. Tesla explains that its motors generate power whenever the wheels turn, so a Model 3 should always be transported with every tyre off the ground, ideally on a flatbed. Its transport mode lets the car roll freely just long enough to be winched aboard.