One big thing is that a 4 wheeled vehicle doesn't meet the legal definition of bicycle in many jurisdictions. Usually the regulations specify 2 or 3 wheels. The 4th wheel makes it a car (legally speaking).
You might get away with it if it were unpowered, but making it motorized pushes it even more toward being carlike.
Another consideration is complexity. A trike has either a single driven wheel or a single steered wheel, so things only get complicated (with differential or steering linkage) at one end.
A quad needs both, a differential between the driven wheels (or single driven wheel on one side, scary stuff when you jack up the power) and a linkage on the steering wheels (plus the need to maintain alignment).