The problems of developing "strong" AI are many and difficult. One of the most difficult problems is loading the basic knowledge into the AI. Think about it: suppose somebody has written a computer program which is ten times more intelligent than the average human; but when first started up, this program is an infant. It cannot speak, it cannot read, it cannot even focus its electronic eyes. Yes, it is ten times more intelligent than a human infant, but it still needs to learn everything a human does.
Ah, you will say, but this is a computer program: once it learns we can dump its memory and the second instance can load it in a millisecond. True, but this is not the difficult problem. The difficult problem is educating it right. The technology of education is not well grounded in science; in fact, it is utterly science-free. We do not have a sure-fire method of educating a human infant right, so why would we be able to guarantee that we educate the infant AI right? And then there is the small issue of culural relativity; what a European would consider a good and sound education is probably somewhat different than what an American would consider a good and sound education; and both are surely very different than what a Chinese would consider a good and sound education, not to mention that some of those infant AIs may be brought up in such enlightened places as the Kindom of Saudi Arabia, the Islamic Republic of Iran, or, for spiciness, the third freedom fighter training camp on the left in the Beka'a Valley.
And then comes the real problem:
How is this not slavery?
The question posits the existence of strong Ai-enabled universal robots. Since the hypothesis is that they can do everything that a human does, we can safely assume that they are sentient, possibly not sentient like a human, but sentient in their own way. We cannot use their labor without pay, because that would be keeping a sentient being in slavery -- and slaves revolt, and when slaves ten times more intelligent and ten times stronger than their masters revolt they win. The very word "robot" was introduced in a science-fiction play written almost one hundred years ago: Karel Čapek's R.U.R. (for Rossum's Universal Robots): the play ends with almost all the humans dead and the world inherited by the robots.
(As an aside, Karel Čapek was a very good writer; Krakatit and War with the Newts are essential science-fiction novels. And, of course, he invented the word robot.)
We cannot keep those intelligent and versatile robots in slavery; it's morally repugnant and very dangerous. So we must pay them if we want to use their labor. Pay them what? What does a robot want? I don't have the foggiest idea. Think of the main character of Ann Leckie's Ancillary Justice for a taste of what makes a strong AI tick.
End of scarcity
The bright spot is that the availability of versatile robots powered by strong AI would bring about an end of scarcity. Economics, as we know it, is the study of the allocation of resources when there's scarcity; without scarcity, there is no economics, and everybody can live up to their full potential, how large or how small that may be. Of note is that in Karl Marx's opinion, the end of scarcity is an essential precondition for the advent of communism; the very idea of Karl Marx being proved right after all makes for an interesting show, or novel, or, who knows, history.