"No Parking" ordinances exist to ensure that the streets remain accessible to the residents, emergency vehicles (fire/ambulance/police) and to facilitate services such as snow plowing, utility systems maintenance, etc. If the street is on a public transit line, it is also intended to create clear areas for safe passenger pickup/dropoff at designated bus stops. In residential side streets the main focus is on access and aestetics. All of these considerations usually don't resonate with self-indulgent boors like your moronic neighbor, but you can take comfort in knowing that ordinances like the "no parking" rules are not subject to action on the basis of petitions. Such ordinances must be applied uniformly throughout the municipality's incorporated area, and street-by-street exceptions are generally not provided for in local law. If they were, they would create an horrendous burden to the city in terms of enforcement.
Ordinances of a minor nature such as parking are rarely enforced as it is -- with the exceptions being in areas where access to municipal facilities would be affected. My guess is that your neighbor has little chance of his petition even being seriously considered by your city planner or supervisor's office -- or whatever your local equivalent would be. Moreover, if he already has five vehicles in his driveway, he may be in violation of an ordinance already. I'd check that out at your city hall if I were you.