It's a cultural thing. In Austria, people build multi-generational houses because it's expected that your kids and grandkids will live in the same house. In fact, Austria only has one city with two million residents - the rest live in mostly tiny towns where everyone knows everyone (and if you're a newbie, that's not a good thing). Anyone who opens up a business, names it after their family. In other words, where you come from is important, and ideally you come from a family that's been in this town forever. So, in a world where your heritage is a disproportionately big part of your standing in the society, geographic mobility is not a universally good thing.

I am sure there are parts of the Midwest that work the same way, but that's by and large not how the majority of the US works. Your heritage is refreshingly irrelevant, and therefore you can move freely from one place to another. Most people realize that big cities offer better career opportunities, and also that big cities suck for retirement. So you essentially see the following migration pattern:

1. [some place where you were born]

2. [your college town]

3. [career-related move to a bigger city]

(this part can repeat itself many times)

4. [retirement somewhere warm and/or affordable]

So if you're going to move somewhere in the range of 5+ times, why would you invest in a multi-generational home?

Finally, as an aside, interesting to note the correlation between the geographic and economic mobility: the American Dream may or may not be alive anymore, but I've seen so many kids from my college come from nothing and make a fortune (and shockingly, kids from good families end up as failures, mostly due to some sort of conflict with their family). I think the society in the US has accepted that there's a lot of uncertainty when it comes to predicting a kid's future.

That stuff simply doesn't happen in Austria on that scale - if you're poor, you'll stay poor, and vice versa. So a good family name leads to a good standing in the society, and the loop repeats itself (this is where your residence can also serve as a signal for your wealth to reinforce that loop). Why risk leaving all that and moving to a new city where you'd be starting from scratch?