So, as an American living in Portugal, I'm not so sure the grass is greener.
It's true that our apartment would be illegal to build in the US. There's only one point of egress in a fire, and it's the stairway we share with our neighbors. That means there's no need to have a long hall like in America, but I'm not really sure the reason prices have ballooned in America is the extra few square feet spent on a little bit of stairway.
There are other ways European apartments are smaller, of course. Even our three bedroom apartment has no linen closet, no laundry room, no closets at all actually. The bedrooms have what I would call extra-large armoires. Again, our three bedroom place is very much built for a family, but the kitchen has a refrigerator smaller than the one my American best friend uses for beer. It's really RV-sized.
Just everything in Europe is tiny. T i n y. And frankly, it's not that much cheaper over here either.
Maybe the extra hall space you need to have two points of egress in a fire is part of it, but that ain't all of it.