I strongly disagree that Functional programming is something that inherently is not suited to building a whole product on. Although I cannot providing evidence that it always is the case, Jane Street is a wonderful example of what happens when a bunch of really smart people get together and use a statically typed functional language to produce a robust piece of software which solves hard problems. Not everything at Jane Street is written in ML, but MANY of the employees write in ML, the software devs, the quants, te systems folks, and even the traders.
Sources http://www.janestreet.com/technology/ Interviewing there Knowing people whir work there