Maybe we're talking about slightly different things?

There are many interesting algorithms that are usually analyzed in an imperative setting, like in-place quicksort, Knuth-Morris-Pratt, or Gaussian elimination. There doesn't seem to be any benefit to analyzing them in an FP setting, because it's not easier and doesn't yield new insights.

It seems to me that the FP approach only really shines on algorithms that are "naturally tree-like". For example, I'm a big fan of Okasaki's work on purely functional data structures, and of Blelloch's work-depth model. But let's not oversell FP techniques as the foundation of all algorithm work.