I then asked him if he could name an example, which he couldn't. I'm guessing that's because there are none, (feel free to prove me wrong) but why is that? Education among developers (or lack thereof)? Lack of performant implementations? No significant advantage? Solution looking for a problem?
It is an interesting question.
Given that both imperative (FORTRAN) and functional (LISP) came on the scene at about the same time (very early 1950) the question can be reduced to "why is the use of imperative programming so much more widespread than functional programming?"
I think there are two possible answers.
Firstly, imperative languages were effectively "higher level" versions of the machine code used to program computers at the time when they were invented, whereas functional languages were effectively an implementation of a fairly obscure branch of mathematics (Church's lambda calculus, which McCarthy was teaching at the time). Thus, imperative programming came naturally to the "old hands" then working the altar of big iron and functional programming limited to a few interest courses in better universities. When CODASYL was struck to determine the way forward for the next several decades, it consisted mostly of "old hands." Thus the foundation for the supremacy of imperative programming languages was laid.
A second possibly answer is that imperative languages are easier for Joe Bitpack to pick up: you don't need to understand about partially-enumerable functions to understand "make this box blue". Since most pointy-haired bosses see all code monkeys as interchangeable, grabbing the first guy to apply who has the right TLAs on his CV and can wipe the drool off his chin most of the time is seen as cost-effective. Natural selection in such an environment gives the reproductive advantage to a paradigm that does not tire out the lips as quickly.
Be thankful. When I was in university I was told that all the old languages were dead and everything would be programmed using 5th-generation languages like Prolog. I am sure my flying car is programmed using Prolog today.