If you created an algorithm that evaluated all possible 32 bit inputs in parallel and then picked the correct value at the end based on the input, you'd still have some funky corner case where the branch predictor in your x64 processor spilled the beans. Are we going to have to design our crypto algorithms entirely on SIMD instructions to combat this sort of thing?
There is likely still potential for side channel attacks. From a 'first principles' approach a computer is always going to leak information about it's current state (power, noise, emi, etc) and the methods / tools / techniques for analyzing that leaking information are only getting better.
The multi-tenant nature of modern infrastructure is the bigger issue in play here.
(I wonder if one is possible if the same key were to be used on different processors, if that would leak certain information, for example.)