They may not have wanted to?
It all depends on the individuals, one family member still lives with their parents and everybody seems to be just fine with it. Not everybody wants to start a family of their own and not everybody looks to get away from home right after they turn 18.
While this clearly never applied to all of the US it applied to a significant part of it.
Now if culture would have massively changed wrt. how family constructs are seen that could explain the increase but AFIK there was no such change.
So in my opinion it's pretty clear that a main driving factor of this increase is that living in your own household has gotten dam expensive. Too expensive.
And yes you can re-frame it as "they don't want to" (because it's to expensive). But that misses the point.
Tuition and health care are also problems, but housing cost disease is the one that is most pervasive and affects the most people.
The root cause is mostly a supply problem due to bad zoning, bad regulations, and NIMBYs. This is exacerbated by prolonged extremely low interest rates flooding a constrained market with cash.
If the economy is bad then you can't move out. If the economy is good well then it is just about to get bad so you can't move out either.
There was never a time in the past that renting didn't eat up most of your money. I didn't know anyone who moved out when I moved out that wasn't also dead broke. This was in the mid 90s though and it was the most magical time to be on your own and young. I don't think I would bother moving out now though if I was young because why pay so much more money just to fuck off on your phone in your own apartment instead of your parent's basement?
The economics are pretty much the same. The culture though is night and day different.
There's efficiency in living under the same roof (unless you hate each other's guts). Especially when you consider how huge and wasteful USA single family homes are.
Scroll down the article a bit and you'll see an age-aligned comparison. The percentage of at-homers has only grown 7% since Boomers stole all the jobs and land.
The relative cost of property/rent to income makes this trend really simple to understand.