It seems we have passed the tipping point for unskilled/blue collar and a good portion of white-collar labor. The future doesn't need the bottom 90% at all.
My guess is that the demand will switch to other services as well, like the nannies you mentioned and better education and other wealthy-person services: personal trainers, nutrition, leisure, party/wedding planners, clothing advisors, gourmet cooking. There will also be a lot of services needed for the elderly.
Of course, competition will be cut-throat, but those jobs that cannot be made more efficient or paralellized (those with a high amount of in-person involvement) will sustain the new middle class.
Yes, people can move to service work but there's not much demand for it. I live near Monaco and the people I know who could easily afford such domestic help tend to get by with less than you would expect.
Besides, do we want it to be 10% has the other 90% working for them doing cleaning and cooking?
What is an example of an industry where gains to productivity don't benefit everyone? Gains to productivity in farming enable the price of food to drop. Gains to productivity in housing enable the price of housing to drop. How does it only benefit the rich?
Even if the price does not drop directly as a first-order effect (such as if the company whose productivity is boosted keeps the difference as a profit), it will eventually through market pressure; a new price equilibrium will be established. In perfectly competitive market (such as food) a competitor will use the productivity boost to lower costs and undercut the first. The resulting competition will lower the market place. Productivity gains lower prices (real prices), benefiting everyone.
Mainly I think discussions of any squishy data set carry a lot more weight once we throw out some outliers and general purpose computers are a definite outlier.
Food production in the US is one of the most heavily subsidized (i.e., artificially manipulated) sections of the economy.
Unless I have steadier access to food, shelter, healthcare, and a safe society, I don't think it should count as a productivity gain or increase in standard of living.
The way I see people used eat, get cured of disease and live how we live today. Without the traditional definition of a job as we know today.
People will have to continue to work to make a living. But it may not necessarily be a job meant in the sense of working for large corporate etc.
In fact, the field has leveled so much, that the rich can't get more bang for their buck. I spent $2,500 on a maxed out MBA, but my super rich friend can't spend $25,000 or $250,000 to get something better. Same goes for iPads, iPods, iPhones, anything in technology.
Another example is Gmail. It's free, and arguably it's the best there is. Rich businessman are stuck in email for most of the day, but they can't do better what I get for free in Gmail. (In fact, they're probably using suckier corporate email.)
It's not food, it's not medicine, but this phenomenon is still pretty notable if you ask me.