No real need to ban old cars, they tend to quickly phase out on their own. Heck, the state I live in has uninstalled all the expensive dyno equipment they used for pre-OBD2 cars because there just aren't enough left on the road to justify maintaining the test. They still sniff, because that's cheap, but not on a dyno.

Given that we still allow horses and Model T's on the roads (aside from freeways, due to inability of century-old cars to maintain that speed), I can't imagine why we'd bother banning them. The nostalgia is nice and their impact is negligible.

I think this policy would ban new sales, not outright ban all old cars.

Both policies exist actually. For instance old cars and motorcycles are getting banned in Paris (outside of weekends IIRC). Even if as the grandparent points out making a new car generates a lot of pollution at least it would reduce the more local problem of having a heavy smog on windless days (and all the health issues that go along with it).

Banning old cars from inner-city driving is a nessesity. With how densly cities pack both cars and buildings, suspended particulate matter is a serious public health risk. But we can still allow them everywhere else where we aren't already struggling with keeping particluate levels at a reasonably safe level.