It’s an amazing theory and it fits a raw observation of the world beautifully.
If we are indeed problem solvers, what is the actual problem we’re solving? Any?
It's essentially an evolutionary explanation, so the problem domain is anything that increases reproductive fitness, yes.
I think that there are some deeply ingrained instincts in our brains like self-preservation. On top of those instincts we add new behaviors learned while we mature and some like reproduction probably are activated at certain age. So basically we have some bounds and we live between those bounds solving problems that arise.