I certainly think that we should show respect to the bodies of the dead though I don't agree with the kind of morbid use of body parts (i.e.,"relics"). We know from Scripture that there is a separation between the body and the soul as for example when Jesus warned about those who could destroy the body but not the soul vs. God who could do both.
My husband is a retired firefighter and he has been present when death happens to a person. He said it is like a light goes out and the "person" isn't there anymore. All that remains is the outer shell - the chunk of dead meat that begins decomposition immediately.
We have a dearly loved senior cat whom I have been preparing my heart to lose one day in the not too distant future. I'm not sure what we will do with her body when that happens.
When we take special care with the body afterwards, it is purely for us, the living, as an attempt to show some respect/love for the memories if the departed.