Heard of it to stop killed greyhounds being identified, when finished racing, but never heard of it with stolen dogs,- those dogs are stolen for breeding or taken well out the area,- and usually dumped when finished with. The tattoo was how one dog was reunited with its owner 18 months later,- had been bred from.
I'd always have mine tattooed,- it won't come back without it. Microchipped also.
You'd soon get pulled walking around with your dogs ears cut off.