We already have a existence proof for useful tasks for which changing inputs do not invalidate benchmark results - namely cryptography, where algorithms must run in constant time to avoid timing side-channel attacks. If your hardware takes a non-constant amount of time to add 8-bit integers, your hardware is broken and should receive a benchmark score of zero. The interesting question is how much overhead would be involved in turning scientific tasks like Mersenne prime search into benchmark-friendly workloads.