There will likely be a point in the future where the abilities of human technology surpass the abilities of humans themselves, making us irrelevant (relatively speaking). We will probably integrate with technology along the way, passing along our good and weeding out our bad, but the end result will be far different and superior to humans. It will be the byproduct of our race, much like we are the byproduct of the first multi-cellular organisms.
Throughout evolution, no species has ever permanently dominated the top of the food chain; it always gets replaced by something else. There's little reason to think that won't happen to us too.
The best I can do is think of Rome's slave based economy. Obviously slaves can do anything the free Romans could, and they did. The Romans were either plebes, dependent on government handouts like bread and circuses, or they were wealthy and then they mostly went into politics.
A Roman slave wasn't much like what we think of as slaves now (i.e. blacks on cotton plantations). Epictetus, for example, was a slave, and who even remembers now who "owned" him?
There were many black artisans in urban areas of the antebellum south who were slaves in just the way that Roman slaves were, doing highly skilled work without personal freedom.
Epictetus is, uhhh, an extremely atypical example of Roman slaves. Most of them weren't kept as pet philosophers.
Most of 'em were working in the fields, most of the rest were serving in their masters' houses, and the majority of the rest were probably doing far worse things (working in the mines or dying as gladiators).
We all retire and let the computers run the economy for us, and devote our lives to the pursuit of happiness, art, love and other non-practical endeavours.
And when the computers start caring about art too, they'll join us, no doubt.
I really hope your vision comes true - I spend too much time thinking that computers are actually going to end-up as the Romans - we'll be their slaves... (pets?)
Mind you, there's another alternative, even more depressing than the one you mention:
90% of the human population finds it impossible to transition to a life of plenty, where there's nothing to do other than enjoy yourself and/or pursue abstract notions, and so a great world war emerges, destroying everything that we've spent a million years of evolution to achieve, and ending humanity's brief reign on this planet.
