Sean -- such an idea has been batted around for at least a few years. The primary issue, in my opinion, is that those who are driving and parking recklessly aren't likely to be the ones who would take an active role in such an organization. I suspect, though with little evidence other than scattered anecdotes, that most active Stormtrack members aren't the ones who are causing problems on the roads. Storm chasing can be a very expensive hobby, not just in monetary terms (equipment, gas expenses, etc.) but also in terms of time. For me, I spent hours and hours and hours looking at models, trying to create forecasts, making early-morning adjustments, dealing with chase logistics (vehicles, chase partners, etc.), taking the entire day to chase and driving to the target. All of this is *before* the actual storm is in view and the chase is "on". When storms move quickly, there may be a relatively small window during which I'm in the best position to view a tornado, and making split-second decisions (changing target storms, picking the best road / route, etc.) can be stressful and can make or break a chase. With so much invested (time, money, and effort), I suspect that all of us want to maximize our opportunity of having a successful chase (for many, "success" means seeing a tornado -- sometimes it can be a relaxing structure chase, etc.). This makes people do crazy things.
In theory, the idea of a formal storm chasing organization is good, in my opinion. However, in practice, I'm not sure it'd be any good. Law enforcement aren't going to start asking for organization ID cards to let those who are "certified" pass a road block. Those who drive most recklessly probably don't care enough about the issue to spend any money joining such an organization. That's not to say there aren't positives to such an idea, however! There just aren't enough of us, I suspect, to make any meaningful impact on the situation.
An organization could try to open a dialogue with local leaders and law enforcement, but all it takes a group of irresponsible chasers or yahoos (or "chasers") to make all of that moot. The problem may not even be the "yahoo" chasers or irresponsible driving / parking habits -- the sheer number of vehicles around a particular storm can be a problem (see pic from 5/19/10) even if everyone is driving legally. I'm part of the problem, as are most Stormtrack members, since we're just one more vehicle added to the mix. Cheap internet makes it easy to go out and watch a storm, at least locally and at least on the high impact days. High gas prices may encourage carpooling (it has for me), but the locals won't care that gas is $4/ga instead of $2/ga if they only need to drive 30 miles to watch a storm or tornado. Pile everyone in the truck, take your iPhone to get video and pics to post to Instagram, and you're good to go.