I don't disagree that there is a lot of conceptual stuff going on behind any proof... but I contend that the same is going on behind logic proofs as well. You wouldn't gain a good understanding of a particular logical system (what motivates it, makes it interesting etc, why we work toward proving the particular theorems that we do) by just working through a set of proofs. Yet logic strives for explicitness in presentation, but mathematics doesn't seem to.

It may just be that you're right and if I ever get that high up in understanding I'll similarly look down upon the plebs and discount their frustration. But consider - if I get that high - I must have used SOME LADDER OR OTHER... the plebs I think, could be forgiven for thinking that the masters are tossing away their ladders as soon as they are done with them.