I first note that there was controversy over disrespect to the Quran by uniformed men/women in the US military during Iraq (and elsewhere); this was problematic for a different reason, in that while in uniform, those people's actions were easily seen as representative of official US sentiment (at least somewhat), in contrast to very clear US direction otherwise. The uniform should be used sparingly when doing controversial things; there is a natural line people can draw between personal expressions of opinion (even those that should be legal, as I believe disrespecting holy books should be) and official ones when the person involved is wearing a military uniform. The uniform is not an outfit for that.
Unlike that case though, I believe the desecration of corpses approaches something I consider to be one of my (reasonably few) strong norms for all humans (that this norm is reasonably common among people today and historically comforts me). This is the notion that corpses are generally to be respected, no matter the character or acts of the person they were before they were a corpse. At death, they cease to be that person, and become generically human. Humiliation or destruction of a corpse no longer can reach them; they have ceased to be a person. It becomes pointless, and catharsis of that sort is ugliness.
I see veneration of the dead as a recognition of the humanity of our form and the dissipation of death as our personhood fades away. We may choose to remember the path of life that led to the good/bad/sometimes terrible decisions people made, but the one thing we no longer can productively do is judge them as we did when they were alive; they are no longer a person and our anger no longer is obligatory or acceptable.
I recognise this is not categorically an argument; it is a conclusion, and an instinctual one at that. It is, nontheless, something I see as being part of our species and not something we have any reason to struggle against; the independent creation of these rules in many contexts by many cultures despite different faiths, millenia of separation, and a plethora of philosophies, combined with no reason to consider it an enemy of civilisation, makes it something we can embrace as part of our shared humanity. And I do embrace it. I am comfortable with it being enshrined in law (which it is in many legal traditions, including ours) and seen with comfort (in contrast to some other parts of human nature) as those of us engaged in self-discovery look in the mirror at human nature. It is not a product of reason, but it is part of human identity.
(I recognise that many of you, particularly those following a rationalist tradition in philosophy, may be uncomfortable that I am not able to/trying to justify it in terms of the public good, or offering a more substantial aesthetic argument. You may be justifiably worried about an appeal to human nature as a reason for part of philosophy, and reject the qualifiers I've carefully placed around my use of that above. I can understand that. I do not have many things I justify by arguments like "that's just part of human nature", and that I have a few like this means it's naturally an underdeveloped and strange part of how I see the world. It sits oddly in my philosophy, as I imagine it sits oddly in the philosophy of others who self-explore. I am not much bothered by this oddness personally; it is a quirk that I accept, even as it is a quirk sufficiently strong that it pushes me into being strongly normative (something I am generally reluctant to be because I think doing that too much makes a philosophy all-elbows).