How important is non-binding site of protein?
As it seems with about everything in protein science, the answer is it depends on the protein.  Many proteins will lose activity if they are truncated; however, I've worked with GPCR's that were truncated down to the extracellular portion only and they showed consistent kinetic results.  Antibodies have been cut into pretty tiny chunks (scFv's) to create some drugs like Pexelizumab. Some proteins can be hacked down quite a bit, some can't be at all.