When it comes to most moving coil cartridges "retipping" is a misnomer. They simply hand you a new cartridge in exchange for the old one. What happens to the old one is a mystery. My guess is that most of them find the round file. I personally would never have a pricey MC like Raul's Lambda SL replaced by anyone other than the original manufacturer.
Vintage cartridges are another story. I have tended to shy away from these as I was never impressed with their build quality. Now, companies like Jico are manufacturing replacement styluses for legacy cartridges with modern materials. Sentimentality finally got ahold of me and I purchased 2 Shure V 15V cartridge bodies with the intent of getting Jico styluses for them. Back in the day the V15 was the cartridge to own and I wonder how it stacks up against modern cartridges. Curiosity killed the cat.