Really O(N!) should nip that in the bud in itself alone. There aren't enough particles in the universe for even 1000 factorial. The scaling isn't trivial at all as the problem space grows and the interactions with itself would start eating up speed further.
While we may one day build computers able of out-competing us mentally in many fields but they would be many different machines and not just one uber-machine for the same reason that we don't try to combine the functionality of a wrench, scalpel, desktop computer, coffee mug, and an assault rifle into one tool. Even if there weren't dangers there would be major costs to it and seriously would you ever do that except as a joke?
OTOH, we have phones, which are telephone, TV, radio, notebook, phone book, calendar, calculator, computer, compass, GPS, camera, video recorder, sound recorder hybrids.
I'm not sure why do you think that algorithms for solving different problems will require different hardware.
What I am saying is that it won't be some magical omnitool that can go from curing death to undetectably forging nanotech instadeath rockets.
Even if hardware is shares configurations will not for the same reason Steven Hawkings wasn't drafted as a general during any of the brief Falkland Islands wars even when they were considering if MAD called for nuking Argentina if they lost.
There are very different specialties even if the hardware is the same. Having superhuman General and superhuman Surgeon skill level would be two seperate major projects to create and with lesser redundancies and in the worst case would call for two modules due to lack of shared synergies. You can't really combine processing and RAM hungry CAD programs with weather simulations and expect to see same memory footprint with the same performance.
While we may one day build computers able of out-competing us mentally in many fields but they would be many different machines and not just one uber-machine for the same reason that we don't try to combine the functionality of a wrench, scalpel, desktop computer, coffee mug, and an assault rifle into one tool. Even if there weren't dangers there would be major costs to it and seriously would you ever do that except as a joke?