Comment by tikhonj

If you start with lambda calculus you don't have effects in the first place, so there's nothing to eliminate. Lambda calculus and friends are perfectly reasonable languages for computation in the sense of calculation.

A better way to think about general-purpose functional programming is that it's a way to add effects to a calculation-oriented foundation. The challenge is to keep the expressiveness, flexibility and useful properties of lambda calculus while extending it to writing interactive, optimizable real-world programs.