I'd point out that some folks say shooting pictures for pay, per client spec, is the exact same antithesis of photographic art that you assign to the competition. We all have our ideas of what is "pure" or "true" art, and any encroachment on that is an affront, but keep in mind that everyone's boundary of offense is in a different spot. And that's ok.
I personally enjoy constrictive competition because it gives me a good chance to think counter to my norms and potentially get something I wouldn't have gotten without the artificial boundary.
I think a problem arises when the organizers of a competition attempt to assign some kind of global significance to their constrictions. The "rules" are only rules in the context of a given community (for example, the entrants of said contest). A good example is APUG's dis-allowance of any non-analog image. It fits the community, but it's certainly not universally applicable to all art, or even all photography.
As to your incredulity about why one would not center a subject, I get the impression that you already know why but are using hyperbole to make a point, but I bet if you do some searches on the infamous "rule of thirds" you'll find plenty of information to wit, and potentially 8 trillion images from 1650 where subjects are laid on the power lines rather than the center line. This, however, does not invalidate a powerful image WITH a centered subject, yet it may answer your question.
Similarly I disagree with you in that an image can be over-processed in the darkroom as easily as in Photoshop. Ok, not as EASILY insofar as the amount of time and effort involved, but my point is that nothing about a darkroom precludes a heavy-handed nincompoop from ruining a perfectly good image by dodging, burning, choosing the wrong contrast, vignetting, masking, colorizing, desaturating, etc. ad nauseum. (Note that said nincompoop had plenty of chances both before and after the print process to ruin the image as well, from bad exposure to the wrong mat color)
Finally, what if a bride asked for off-center compositions with subtle, soft light?