They may not need to ban old cars outright. Instead, they'll just kill them off quietly - by poisoning them internally. With ethanol.
Modern cars - cars built since the early '90s - can stomach the stuff . They have engines designed to deal with corrosive, ethanol-doctored "gas" - and peripheral systems (hoses, seals, o-rings, lines, etc.) made to withstand it. Being computer controlled, they can also adjust themselves to deal with ethanol-laced gas. They may not get the best mileage they're capable of delivering - because ethanol is less energy dense than gasoline - but at least they run ok.
But with older cars - cars built before the early '90s, before widespread use of ethanol-doctored fuel - you've got two problems. One of them is relatively minor - and easily fixed. The other's more serious - and not easily (or inexpensively) fixed.
The minor problem relates to the older (pre-early '80s) car's static engine operating parameters. Meaning, they can't self-adjust like a modern car's computer-controlled engine to compensate for different fuel type and quality. They're mechanically set to run a given air-fuel ratio, ignition timing and so on - all assuming a given type of fuel. In the case of of early '80s and older cars, that means regular unleaded gas - not mostly gas and 10 (or 15 or 85 ) percent ethanol.
If the type/quality of fuel changes, but the engine isn't adjusted to compensate, it won't run as well it should until it is adjusted - or it's fed the original type of fuel it was designed to burn. If it's not adjusted, what typically happens is the engine runs lean when it is fed ethanol-laced fuels. One result of that is it will run hotter. This was precisely what was intended - openly - when "oxygnates" such as ethanol and MTBE were added to gasoline beginning in the late '80s and early '90s. It was a way to lower the tailpipe exhaust emissions of pre-computer-controlled car engines - because they could not adjust themselves and in this way, the fuel altered the operating characteristics (and exhaust byproducts) of the engines in those cars.
The downside - in addition to the noticeable reduction in gas mileage that resulted - was that these older engines were often harder to start, would not idle as smoothly as they did previously, tended to stall more - and lost some horsepower, in addition to the drop in gas mileage. An engine that's made to run hotter than it was designed to run will also tend to wear out faster.
The fix for this is fairly easy. You (or your mechanic) simply adjust the carburetor to run richer, alter the ignition timing - and so on. Now the engine will run ok - even though it probably won't give you the gas mileage it otherwise would have - just like any new car force-fed ethanol.
Once computer-controlled engines came into widespread use beginning in the mid-late 1980s, the need for ethanol-oxygenates as a form of emissions control vanished - because these cars would automatically adjust for the leaner fuel they were being fed. Of course, the use of ethanol was not discontinued. It was expanded. Today, most "gas" is actually 10 percent ethanol (vs. 5 or so at first) and there is talk of upping the ratio to 15 percent ethanol. And that poses a serious threat to the well-being older (pre-'80s) vehicles.
Such vehicles are vulnerable to alcohol-caused fuel system corrosion (think gas tanks, steel fuel lines) as well as potentially catastrophic fires resulting from seepage around seals and from hoses/rubber diaphragms (as in mechanical fuel pumps) not made to withstand high-alcohol-content fuels. The only fix is to physically replace all the affected parts with new parts made to handle alcohol-heavy fuel. This can involve a great deal of expense - enough in some cases to make it not worth doing. A new gas tank, steel lines, fuel pump, flexible hoses and rebuild of the carburetor with new gaskets, floats, power piston, etc. can involve $1,000 or more just for the parts - and if you have to pay someones else to install them, much more than that.
The main effect, unintentional or not, will be (has been) the accelerated retirement of not-yet-restored older cars still being used for regular transportation. Or just sitting (really bad news if there's alcohol-laced "gas" in their systems). The more ethanol they put in "gas" - the worse this will get. Especially if "gas" shortly becomes 15 percent ethanol - as seems likely.
Restored classic cars will have been updated with the new, alcohol-friendly parts because that's all they sell now. But the not-yet-restored ones will deteriorate more rapidly, which will mean they'll get thrown away sooner. This means fewer "project cars" and "parts cars" available - and higher prices for the limited pool of already restored/well-kept older cars, just as Uncle Sucker's Cash for Clunkers has markedly driven up the price of clean late model used cars.
So, we're facing a much more subtle end-run assault on the pre-computer, pre-"safety" automobile than getting laws passed that directly target them - such as laws requiring they meet current emissions standards or that they be retrofitted with air bags and computers and all the rest of it. Just kill them off, quietly - by attrition.
The Clovers who hate old cars may have taken a lesson from the Clovers who hate firearms. Rather than ban guns, they are shifting their efforts to bans on ammo.
A gun without ammo is as useless as an old car with an ethanol-rotted engine/fuel system. Mission accomplished.