I’m by no means an expert, but there is no technical reason you couldn’t use a controller like that. I think generally people just prefer the steering wheel controller. Joystick controllers like above are generally designed for airplanes, helicopters, quads and the like. The more sophisticated ones allow mixing so that one control adds in a bit to one or more of the others for the more complex control surfaces of airplanes.
For a car, you assign one channel to throttle, and one to steering (usually updown for throttle, leftright for steering). The one additional complication is that some controllers don’t have “spring return” on the traditional throttle stick, so if you let go of the controller, your car will keep going. on airplanes and quads, this is considered a good thing, as you don’t want them to drop from the sky.