No one needs to prove you wrong because that's not where the goal post actually is.

You could craft hand written assembly code which will be faster than optimised C code most of the time yet you don't. Plenty of programmers are perfectly writing imperative code in Java doing a ton of necessary boxing and unboxing. It's all a trade off between performance and usability. The fact is that the Ocaml compiler does a good enough job with functional code that its performance is actually comparable to imperative solutions most of the time.