Millions of animal species with uncountable numbers of individual specimens live on this planet. Their individual worth is often defined by the local value / significance they have for humans, which differs culturally and individually. While it is currently socially accepted in some Western countries to lament the passing of an individual pet dog or cat and give it a funeral comparable to humans, doing the same for the cattle used to feed said cat or dog isn't. Neither would be elegies or funerals for the endo- and ectoparasites of the cat / dog killed by the respective veterinarian, wouldn't they?
Animals are animals, not humans. That does not mean that you should treat them disrespectfully or even mistreat them. There is, however, little to no evidence that animals understand the concept of an afterlife, respect for a dead body (your beloved dog, and most definitely the cat, would probably dine on your corpse if starving) or see the necessity of a funeral ritual. The latter is first and foremost a human necessity in most cultures / societies. To bury dead pets properly is both important for individual human grief coping and Public Health. Public Health, disease control and hygiene are also the main reasons for disposing of animal corpses in populated areas. Just keep in mind that in some countries, privately taking away roadkill to give it a funeral could be considered poaching, once huntable wildlife is concerned.
If the corpse of an animal can have an educative or memorial purpose, I see no disrespect in having it prepared professionally.