The idea behind "open plan" spaces is to make it seem more roomy by combining rooms and not having so many walls. People are both larger and taller than they used to be, so tiny houses can seem claustrophobic. Combining your living areas (living room, dining room, kitchen) into a single space actually makes sense here. Americans don't even use formal dining rooms any more, so it's a waste of space to have them, so now they're either eliminated altogether or made part of the living room or kitchen (the so-called "eat-in kitchen").
Now, as for Americans' "obsession" with open plan, this does not apply to offices; the dynamics behind house design and office design are completely unrelated. For houses, it's because people want a more spacious feeling, like I said above. For offices, it's because corporations are cheap bastards who want to save money on office space for their office drones, so they've made up a bunch of nice-sounding BS about "collaboration", when the real motivation is to greatly shrink the amount of square footage per desk because the open-plan concept lets you shove more desks together more closely, and commercial real estate is expensive. There's also a certain amount of managers liking to be able to see what their employees are doing. In reality, open-plan offices absolutely kill productivity for workers who need to concentrate on their work, such as software developers.
Central/Eastern European apartments often had a small foyer, a narrow hall way, and doors along the perimeter into ~2-3 rooms--sometimes more. The hallway usually had closet space. One room was generally somewhat bigger than the others and understood to be a "living room". Kitchens were separate rooms and often had a door of their own, which effectively meant they were an additional room, since one could work, study and socialise at the kitchen table. Overall, there was much more compartmentalisation and walls, which I think is essential if you have children, but even if you don't. Interestingly, I wouldn't say their area was much bigger than 1-2 BR apartments typically found in America--the floor plan was just configured much more rationally. Such apartments were fairly close to table stakes in former socialist bloc countries, as well as elsewhere in central Europe.
For instance, my wife and I live with our three young children in a 2 BR ~1200 sq ft. unit in downtown Atlanta--definitely against the grain. It's the typical American apartment layout, a poor and awkward imitation of a house; front door that opens into an "open plan" consolidated living room and kitchen environment, and two bedrooms where "private life" is said to take place.
What would make far more sense to me would be to take that same 1200 sq ft. and dump the second bathroom and the unnecessarily large walk-in closet in the master bedroom. That would certainly provide for a third--if small--room that could be used as a study, which would literally make all the difference for allowing me to get at least some work done at home. And we don't need a giant "TV room"; what we need are walls, noooks and crannies. It's wasteful and pointless; it leaves us with two bedrooms that are really only good for sleeping, and one common area in which all five of us have to coexist much of the time. Might as well just get a large studio at that point.
As I see it, much of the problem with "open plan" offices carries over into "open plan" floor plans. I don't understand Americans' obsession with and preference for this design. It's perfectly possible for families to live comfortably in a central urban place with relatively little square footage--if it were designed more sensibly and with some of the virtues that otherwise can be found only in a freestanding house.