The car must be registered and insured.
I'm actually starting to like the USA again...
Cars are registered and insured in the US at the state level, the federal government isn't party to it. Frankly, even at the state level, insurance is not filed with the state unless you have prior convictions of lacking required insurance (then you have to file a SR-22, at least in Texas).
My auto insurance is between me and my insurance company, I have a card to show a police officer if pulled over that I carry at least the minimum required coverage, but the government doesn't know how much, only that I have "enough".
As for a "wealth tax", are you serious? Blah... if it is taxed when I earn it, then you can't have another go at it, that is the whole idea of no double taxation. We fought a war of independence to rid ourselves of such nonsense. Of course, we have the death tax, which is clearly unconstitutional, but seems to be ignored anyway, so perhaps I shouldn't talk. Stupid government not following its own rules.
As far as insurance goes - you only need to have liability insurance. If you want to insure your car for theft and damages, that's voluntary - but being able to pay for damages caused by you isn't. And as Norway is a rather small country, rather than a federation of states, expect it to have information and powers that you'd usually think would would be separated by "federal" and "state". You get a sticker every year showing that the yearly road fee is paid, and that liability insurance is OK.
Wealth tax has some bad side effects - like most taxes - and fortunately, the new government is working towards removing it. However, the Norwegian tax system is in general more sane than the US system - lower rates and less loop holes - so it isn't all bad. And more importantly, Norway has a healthy budget surplus - the key to any sane tax cut.