Eh. I'm not sure I'd call it appearance only. In some parts of "the West" (notably the Roman Republic and early Empire, but it went on a for a long time after that) adult adoption as a succession/continuity-of-business mechanism was commonplace.
Notable Roman examples include the _first two emperors_ (Augustus/Octavian was adopted by Julius Caesar, Tiberius was adopted by Augustus. Tiberius also had both an adopted and natural son; given that the adopted one was adopted before the natural one was born, he was the heir, giving some indication of how seriously this was taken. (Ultimately they both died)
Even in medieval and early modern Europe, legally adopting apprentices etc wasn't uncommon.
This is the same mechanism that business succession planning reduces risk. Failure to train and groom new talent for leadership roles is a good way to ensure a company dies with its current staff.
Yeah, generally, but they're just the most famous examples (because emperor); this was standard behaviour for the time if you had something to pass on and didn't have kids. Adopting adult men was really commonplace in Roman society; Roman infant mortality was _astronomical_. The Japanese adoptions mentioned above were pragmatic, too.
Arguably, it's unfortunate that the custom died out for European aristocracy (though it did continue to some extent for normal people). A _huge_ number of wars were caused by failure to produce an heir.
That's why the kids aren't interested in taking it over. It's not a route to generational wealth for anyone who has regular middle-class opportunities, as much as it's a route to being busy all the time, and having nothing to show for it at the end of the day.
Businesses that actually have real prospects frequently get taken over by the kids. The family shop/bakery/restaurant is rarely one that has them. You don't want to be doing all the work in a line of business where the prevailing pay is minimum wage.