OK, so pre-existing general computational problems likely cannot benefit. But if someone were to design a new system with carte-blanche, what constraints on tha

OK, so pre-existing general computational problems likely cannot benefit. But if someone were to design a new system with carte-blanche, what constraints on that system's design would still allow them to exploit all this mining hardware? Put another way, what designs are to be avoided, lest an army of re-purposed hardware be launched against them? For instance, is SHA256 slightly weakened because brute-force is orders of magnitude less difficult now, than it would have been sans specialised BTC hardware?