Watching one of the many court shows where a woman brought her cat in to be freeze-dried to preserve it. It's really obvious that this woman was really into her cat, and what she wanted was to get her cat back so that it looked like it was just sleeping, and there really isn't any way to do that without some pretty effective and artistic taxidermy, and this woman wanted no "foreign substances" within the cat's body.
But when I think of keeping a dead pet's body around... that's not the part of the pet that I loved. I loved the cuddling, the interaction, the playing. That's not something that you can recapture through freeze-drying.
There is a perverse part of me that after I die, wants me to be freeze-dried and mounted in a chair with a beer in one hand and a remote in the other. I think I'd prefer plastination. Another option would be to be mounted in a pose like a grizzly bear so that people could hang their coats on my outstretched paw.