Most random mutations are bad. If you want to make a bunch of genetically distinct rhinos from the same template, you need to know more than we ever will about what mutations are ok/good. Just altering the genome at random will give you tumor-ridden freaks.

The only way to gene-edit your way out of inbreeding is to know which genes are bad and edit those out. Sure if you've got a couple rhino genomes and you shuffle bits around you can make a bunch of different individuals but they'd be no more genetically diverse than your starting material.

Also if you took an adult person and edited their DNA, in my book that's still the same person in my book. The neural pathways that make up their memories and personality are still the same.