>people tend to keep shitty cars much longer than rational, because they cannot afford a better car - throwing away all the emission savings

Keeping an older car rather than buying a new one is often the more environmentally sound decision, because it takes a very long time for improved efficiency to break even on the massive environmental investment of manufacturing the new car.

> It lead to too many small cars(VW Up, Seat equivalent, and the like) because that's what common people can afford

Slightly confused - what's the issue here? Small cars are good. They take up less street space and tend to be more economical. My wife owns a Fiat 500 (which is about as small as you get); it's much easier to park on the narrow streets of our rural town than a bigger car would be, its fuel consumption is stellar, and it's no bigger than we need.

> Another side effect is that people tend to keep shitty cars much longer than rational, because they cannot afford a better car - throwing away all the emission savings in the wind(pun intended).

Here in Norway the car has to pass quite strict emission standards (EU kontroll) every 2 years or it will not be allowed on the road. I think you have the same thing as it's from EU. So the amount of old clunkers that pollute should be minimal, mostly limited to veteran cars (25+ years in Norway) which are exempt.

> they cannot afford a better car - throwing away all the emission savings

Buying a new car for proportionally lower emissions is a false economy as much of the carbon footprint of a car is in its manufacture, not just its use. Holding onto older cars that aren't offensively inefficient (e.g. any small hatchback) seems environmentally responsible to me.

Agreed, the tax is not ideal. It's better than nothing..

But it would be even better if we somehow could tax households higher for their second car.

In practice it's probably an administrative nightmare with too many loopholes.