IIRC, that's wrong. The documentary said that Japanese tradition is that the eldest son inherits the father's business. Jiro has two sons, so he created a clone of his business for the second. They're literally exactly the same layout except mirror images of each other.
The poignant thing that I remember is that the person who actually made the sushi for the reviewer who made the restaurant famous was not Jiro, but his son. And the wondrous thing was that the enterprise wasn't about chasing fame or fortune, but about being dedicated to excelling at a craft.
Closest thing we have are the arts, and there's the meme about the starving artist here because most artists struggle to get by, or end up having to do commissions for others (I hear furry porn is lucrative) so they don't get to do what they want.
Meanwhile in Japan you get 1000 year old roadside snack shops, brushmakers, a watchmaker that spends a year holed up in his apartment to produce a single watch, etc. That's the 'PR' side of Japan anyway, on the other there's the 14-hour workday wage slaves.
The West includes the Amish, where inheriting your father's farm, and with it a centuries old tradition, is the norm.
Meanwhile, Japan underwent modernity just like everyone else, and there, the modal (male) life story is: get a lifetime job straight out of college, and work insane hours for the rest of your life, or don't, and never get a job worth having.
There's a lot to learn from Japan, particularly about excellence in craftsmanship, and it's easy to romanticize this, particularly for those of us from countries which are only a couple hundred years old.
But I've been to a pub in Nottingham, ye Olde Trip to Jerusalem, which claims to have been founded in 1189 (superb ale by the way). Swiss watchmakers, French cognac distillers, Chartreuse, even Harvard: all of these things are closer to that tradition of continuity and and craftsmanship than the starving artist stereotype.
The 2nd son didn't inherit under the doctrine of primogeniture, leading the later sons to be the (often) neglected or less favored / wealthy, motivating them (for better and worse) to set out on their own and prove their worth.
Inherit, clergy or war.
Extra sons were, yep, often sent off to war. They'd either conquer their own territories or be killed. In either case, they were no longer a threat to the primary heir.
I saw another show about a small ramen shop owner who took a half day off a week and never went on a vacation for 5 years straight. That sounds more like prison than a job.