I can't speak for anyone else, but I can think of one reason to do things like this. If I can use a minimal subset of language features and verify their correctness, and also verify the correctness of the ways in which I combine them, then it would follow that my entire program is much, much easier to prove correct.

This is perhaps more useful in lisps or Haskell but it's still cool to think about. And, hell, maybe someone implementing a language in C could do something like this for the debugging properties.

And while yes you could take this to the extreme and implement everything on top of SKI combinators, perhaps one wants to start a touch higher up than that. Anyway, maybe that's a useful answer?