Why do you speak about EU/Europe as a whole? There is no such thing. I thought it is, but, now, when I moved to "Europe", I see that ti was illusion.
Prices are different across countries. Do you think Poland, Portugal and the Netherlands have same prices? HA! Compare prices in the Netherlands and its neighbor Belgium. I didn't compare prices for (new) cars, but I did for new motorcycles. Difference can be up to 20%. And it is two of three countries which are known as "Benelux", not two countries on different edges of EU.
Choice is difference between countries too, there are models which are present in one country and not in the orthers. Heck, even selection of a food is drastically different in two Lidls (two supermarkets of same chain) on different sides of Netherlands/Germany border in 10km vicinity!
Many people say that they see that almost all new cars they see are BYD & others — there is no BYD in Netherlands, for example. There is Lynk & Co (which is Volvo / Geely / Zeekr), and it's all of Chinese brands.
There is no such single entity as "Europe" or "EU". Different countries are very different in available goods, prices, taxes and regulations. Yes, there are global things, like GDPR or emission regulations (Euro 5/Euro 6), but still there are a plenty room for difference.
And even "single economic area" is illusion: you cannot simply register car or motorcycle bought in Portugal or Belgium in the Netherlands, you need to pay local VAT, local ecological taxes, etc. So no, there is no "lifehack to buy car or motorcycle in Belgium and save 20%.