There seem to be a lot of people confusing complexity with practical issues.

I think we can agree that: 1) you can write most software in a functional programming language without any (noticeable) loss of performance 2) there will always be software (video encoders, HPC stuff) that will always be done in Fortran/C :D

However, I think the question is very interesting from a theoretical point of view: if you model imperative algorithm as programs for a RAM machine (good theoretical approximation of real single core computers) and purely functional algorithms as programs for a TBI machine (good theoretical approximation of a hypothetical machine executing pure algorithms), is there a problem for which a faster solution exists for a RAM than for a TBI?

Note. RAM machines exist and are standard in literature; to my knowledge TBI (to-be-invented) machines do not (yet) exist.