Depends on what would satisfy us, I suppose.
It might turn out that what does satisfy us is to be "free", to do what we want, even if that means that we will mess up our own future. It might turn out that humans are only satisfied if they can work on existential problems, "no risk no fun". Or we might simply want to learn about the nature of reality. The mere existence of an FAI might spoil all of it. Would you care to do science if there was some AI-God that already knew all the answers? Would you be satisfied if it didn't tell you the answers or made you forget that it does exist so that you'd try to invent AGI without ever succeeding?
But there is another possible end. Even today many people are really bored and don't particularly enjoy life. What if it turns out that there is no "right" out there or that it can be reached fairly easily without any way to maximize it further. In other words, what if fun is something that isn't infinite but a goal that can be reached? What if it all turns out to be wireheading, the only difference between 10 minutes of wireheading or 10^1000 years being the number enumerating the elapsed time? Think about it, would you care about 10^1000 years of inaction? What would you do if that was the optimum? Maybe we'll just decide to choose the void instead.
This is a different context for satisfaction, but to answer your questions:
yes, I often find satisfying working through problems that have already been solved, though I appreciate that not everyone does;
no, I would not want to be denied the solutions if I asked (assuming there isn't some other reason why giving me the solution is harmful), or kept in ignorance of the existence of those solutions (ibid);
if it turns out that all of my desires as they currently exist are fully implemented, leaving me with no room for progress and no future prospects b
Barring a major collapse of human civilization (due to nuclear war, asteroid impact, etc.), many experts expect the intelligence explosion Singularity to occur within 50-200 years.
That fact means that many philosophical problems, about which philosophers have argued for millennia, are suddenly very urgent.
Those concerned with the fate of the galaxy must say to the philosophers: "Too slow! Stop screwing around with transcendental ethics and qualitative epistemologies! Start thinking with the precision of an AI researcher and solve these problems!"
If a near-future AI will determine the fate of the galaxy, we need to figure out what values we ought to give it. Should it ensure animal welfare? Is growing the human population a good thing?
But those are questions of applied ethics. More fundamental are the questions about which normative ethics to give the AI: How would the AI decide if animal welfare or large human populations were good? What rulebook should it use to answer novel moral questions that arise in the future?
But even more fundamental are the questions of meta-ethics. What do moral terms mean? Do moral facts exist? What justifies one normative rulebook over the other?
The answers to these meta-ethical questions will determine the answers to the questions of normative ethics, which, if we are successful in planning the intelligence explosion, will determine the fate of the galaxy.
Eliezer Yudkowsky has put forward one meta-ethical theory, which informs his plan for Friendly AI: Coherent Extrapolated Volition. But what if that meta-ethical theory is wrong? The galaxy is at stake.
Princeton philosopher Richard Chappell worries about how Eliezer's meta-ethical theory depends on rigid designation, which in this context may amount to something like a semantic "trick." Previously and independently, an Oxford philosopher expressed the same worry to me in private.
Eliezer's theory also employs something like the method of reflective equilibrium, about which there are many grave concerns from Eliezer's fellow naturalists, including Richard Brandt, Richard Hare, Robert Cummins, Stephen Stich, and others.
My point is not to beat up on Eliezer's meta-ethical views. I don't even know if they're wrong. Eliezer is wickedly smart. He is highly trained in the skills of overcoming biases and properly proportioning beliefs to the evidence. He thinks with the precision of an AI researcher. In my opinion, that gives him large advantages over most philosophers. When Eliezer states and defends a particular view, I take that as significant Bayesian evidence for reforming my beliefs.
Rather, my point is that we need lots of smart people working on these meta-ethical questions. We need to solve these problems, and quickly. The universe will not wait for the pace of traditional philosophy to catch up.