I've suggested before that "proofs" should be thought of as a sort of "table of contents" of an argument. One thing I was getting at was that while they give the appearance of clarity and neatness, proofs very often serve to conceal major issues (meanings of words, background assumptions, etc.). Because of this, clarity can help prevent understanding. To put it another way, a very clear, concise argument can cause us to accept (or reject) the argument before we put forth a major effort to understand the argument.
I think it's fruitful to think of the desire to find proofs as an element in cost-of-reasoning reasoning. As a practical matter we simply can't reason out every little thing; having a proof already in hand allows us to jump safely from point A to point B without worrying too much about intermediate steps, and by boiling things down to bare essentials the proof itself enables us to avoid distractions, tangents, and red herrings. But cost-of-reasoning reasoning always has its dangers: it may lead to overlooking important things, or, in a case like proof-finding, to placing excessive importance on things that are easy to prove, just because they are easy to prove, or any number of other things. By thinking of a proof as a table of contents to a more thorough and elaborate discussion (including what its conclusions are relevant to, the assumptions that make its steps good one, the intelligibility of its premises and the reasons for starting with them, the end in view when reasoning in this way, etc.) we can avoid some of this danger. In the case of some proofs, of course, the more thorough and elaborate discussion won't be all that much more elaborate, or at all interesting; but for others it certainly will be.
