It depends on where you are. Public transit in London, for example, is amazing. The longest wait for a train at my local station (Zone 2) was around 12 minutes off peak. Night buses take over for the tube late at night. They'll take you where you need to go, albeit a little slowly. A yearly pass costs £1216 (Zone 1-2). Good luck getting insurance and petrol for much less than that.

There's an argument to be made that public transportation isn't available because poor and middle class people can afford cars.

Note that we hardly have poor people (by American standards) because of the welfare state, which is partly funded by these extremely high taxes, but it is difficult for low income people to afford a car (gasoline is heavily taxed too). If they really need it they will buy an old beater and drive it a couple of years until it dies, then repeat (which somewhat nullifies the rationale of car registration fees helping the environment).

The 180% is for private cars. They give breaks for vehicles with special registration (commercial, foreigners etc.), I guess to not stifle business / foreign workers too much.

I think the rationale for the high fee is (a) Denmark likes taxes (around 50% income tax on average) to run our comprehensive welfare state, and progressive taxation that taxes wealthier people more is seen as the best approach (new car buyers sort of fit into this), and (b) "the environment", we have very good public transportation (and, famously, bicycle facilities) which the government wants to encourage.

I don't agree 100% on those points but there it is.

Yeah, searching a bit suggests that the huge tax is on the purchase, not an annual thing.