Assuming such a petition would influence NASCAR to remove the restrictor plates, without some solid plan of steps to provide competitve racing and keep speeds at or near their current levels such a thought if fruitless.
I'm sure many tire of my references to the past, but it is from the past that many of todays policies and regulations draw their sustenance. So first a look back at one of the early challenges to the very existence of NASCAR, the second one actually but most germaine to this issue.
May 19, 1957 there was a 250 mile Grand National event run at the Martinsville Speedway. Billy Meyers was leading the race in his Mercury when he collided with a lapped car driven by Tom Pistone. Meyers' Mercury was sent spinning and cannonballed through the guard rail and a fence becoming airborne. It never should have happened. There was a big sign right there that clearly read "NO Spectators". But there were people gathered around that area to enjoy an up close view of the race and Meyers car struck seven of them. Four people were seriously injured, including an eight year old boy who suffered critical head injuries. The race was red flagged to let the medics attend to the injured and never resumed because of rain. The wire services and other media quickly broadcast the tragedy in time for the evening news and morning papers. Most accounts included a note that Meyers was driving a Mercury, and that's not the sort of publicity the auto maker needed. In retrospect it seems difficult to lay blame at the feet or Meyers or Mercury, and fault lays with whatever adult bought the little boy into such a dangerous area, but the car companies were horrified and even those besides Mercury knew that the next such incident might involve one of their cars.
A few weeks later the AMA met, and on June 6th, 1957 they reached an accord. All the major auto manufacturers agreed that they would no longer have any association with or support auto racing of any sort. Overnight all that factory support money dried up. There was real concern if stock car racing could survive without that factory money, because even then, as today, the race purses alone just weren't enough to support a team even if they ran well. That complaint seems to have been around as long as NASCAR. But at that critical juncture, with the future of his sanctioning body at stake Bill France stepped into the void and immediately convinced promoters that they needed to increase their purses if the sport wanted to survive, and NASCAR itself guaranteed that any team that came to a race would earn at least 300 dollars. 300 dollars, "Travel money" as it was called, may not sound like much but racing was much cheaper then. The payment of Travel money cost NASCAR a good chunk of it's profits, but Bill France had enough foresight to see he was investing in the future of his sport, and that investment eased the transition of the sport after the factories packed up their fat wallets and went home.
One of the reasons that NASCAR continues to mandate the unpopular restrictor plate rules is a fear once again a race car could go into the crowd, which once again could put the future of auto racing at stake. A horrific accident would no doubt once again set the short sighted politicians and gloom and doom safety advocates scrambling for a seat on the bandwagon to ban auto racing, and the media into a feeding frenzy of lop sided reporting with lurid footage of the accident. The ability to participate in and watch the sport we love may seem a freedom guaranteed to us all, but the cost of freedom is eternal vigilance.
With the ever growing litigousness of todays society, even if the politicians, manufacturers, sponsors and press could be endured, the rash of lawsuits and civil actions brought against the sanctioning body could very well bankrupt the sport entirely. And the sad fact is that most lawsuits would be likely be won. NASCAR has through its actions tacitly admitted the possibility of a racing vehicle entering the stands at the speeds un restricted cars would be capable of. Add that events of the 80's demostrated that fact even further and a very legitimate basis for negligence is established.
NASCAR to its credit is working hard to find an answer to the plate problem. The testing which has gone on at Daytona and its sceduled to continue is pursuit of just such a resolution. The simple act of removing the restrictor plates is in IMHO not viable.