Yeah, there isn't free flow of car registration in EU or within its Schengen area. If you buy a car in another EU country you need to register it in your country of residence and it will be taxed and slapped on with various fees according to local rules.
Another example, if you move from let's say Germany to Denmark, it's incredibly easy in many ways, but not when it comes to your car. You're allowed to have it on your German registration papers for 6 months, then you have to register it according to Danish rules, which comes with a hefty tax payment. You can choose to not do that, but then whenever you get pulled over by police, they will check the papers and fine you heavily for not registering the car in Denmark. Many expats decide to not bother at all and just sell the car in their home country.
There may be a loophole somewhere, but for the regular person there is no avoiding the taxman.
Another example, if you move from let's say Germany to Denmark, it's incredibly easy in many ways, but not when it comes to your car. You're allowed to have it on your German registration papers for 6 months, then you have to register it according to Danish rules, which comes with a hefty tax payment. You can choose to not do that, but then whenever you get pulled over by police, they will check the papers and fine you heavily for not registering the car in Denmark. Many expats decide to not bother at all and just sell the car in their home country.
There may be a loophole somewhere, but for the regular person there is no avoiding the taxman.