If robots do most jobs, and 90% are eliminated and not replaced, we could all have 4 hour work weeks, but with the same total pay (i.e. everyone would make 10x the current hourly rate). The economy would support it. But with our current system of economics, private property, and of course overtime laws, what would happen is we would have 95% unemployment, and the last 5% of people would work 40 hour weeks.
You seem to be saying the last time automation really look off, the long-term effects were, for the majority of working people, a reduction in working hours to the 9-5. Free time, weekends etc. Jobs were lost, and never replaced, because we all just look more leisure time. I totally agree.
But, you are saying that when it happens again it would be different because of "our current system of economics, private property". But think of last time this happened. Ownership was concentrated among a tiny tiny elite. In Victorian England, at the time of the Industrial Revolution, landowners, and then an emerging bourgeois of business owners controlled everything, including voting rights.
So I don't understand what you think is different this time around? (not being argumentative, I actually can't understand). Is it unions? Because to me, wealth seems less concentrated than it used to be (pre-industrialisation, when the Aristocracy owned everything and we were just allowed to subsistence farm their land for a cut of the crops). I should fact check though, because perhaps I'm making an assumption and wealth is now more concentrated. Maybe the difference is corporations v. aristocratic families. Is that it? Corporations can build much more wealth, whereas the Duke of Devonshire can only own so much land before he meets the boundary of the Earl of Strafford*?
*locations not historically accurate because I'm mixing up time periods, but you get the idea.
I'm not sure how to find data for pre-democracy empires and aristocracies (what with factoring not only inflation but exchanged rates to no-longer-in-existence-currencies - it is unlikely to have ever been much more unbalanced, because pre-industrialization there simply wasn't as much total wealth in exsistence) but we are in fact at the worst wealth inequality our nation has ever seen

The last time it was this bad, we did change the system.
We started regulating banks (Glass–Steagall, FDIC) and the stock market (SEC).
We created the social safety net - Social Security, food stamps, and the FHA.
This was when we outlawed child labor, instituted the 40-hour work week, and created the first minimum wage.
It was when unions started to be strong enough to have real influence.
Public Works was created, providing many major projects (the San Francisco Bay Bridge, the Lincoln Tunnel, La Guardia airport, hydroelectric dams, schools, hospitals, the nationwide electric network, etc) on the federal level.
In other words, really major reorganization of how we as a society handle economics, labor and wealth distribution.
Some of these changes lasted to this day - others have been repealed or gradually pushed back, which helped bring us back to where we were (and helped trigger our recent recession)
Obviously there was a long time between 1820 and 1920 - but the peak of the graph didn't happen overnight. Both the technology and the effects took time to fully establish (Ford's assembly line wasn't until 1913). Those steps 100 years after the revolution were a large part of what made the graph above peak, instead of continuing to climb.
What is different now is that while business and the rich strongly objected to those changes when they happened, a majority of ordinary middle class working Americans supported them.
Today half of Americans have principals with align with the interests of the rich - individualism over shared prosperity, and economic growth at all costs (regardless of how the benefits of that growth are distributed). I don't think, politically, something equivalent to the New Deal could happen today.
This time part of the run up of concentration of wealth is due to computers (along with political changes giving corporations and banks more freedom, repealing Glas-Stegal, encouraging outsourcing as "free trade", etc).
But so far robots have only been able to take fairly menial jobs.
We've still got some time before we get to 100 years from when this new revolution started
Its probably just a coincidence that the graph starts going back up the same year that the TRS-80, Commodore PET, and Apple II came out, but it is certainly a funny one to underline my argument!