Stealing a car is not the same as stealing a candy. In Europe all parts are marked so it takes significant effort to sell or modify such cars. It's not like people steal them and then sell it at yard sales.

As for the "beaters": shortly after Russian invasion on Ukraine plenty of cars were stolen in Poland. Not the expensive kind but usually 10-30 years old cars with big and reliable engines (V6, V8). I know 6 people that had Jeeps Grand Cherokee stolen (different generations).

My uncle wanted to renovate Isuzu Rodeo with completely rusty frame but V6 engine of a value of like 300€ and it was stolen too.

And it happened ~1 month after it started.