Don't try to fix something, if it's not broken. Paper and ink have proven to be effective means of backing up private keys (seed phrase). Having multiple backups helps to act as a fail safe and should be encouraged too, but I can't see a single need to want to carry my seed phrase around in my tooth implants.
What would be the pros and cons of this one?
The biggest con is that a regular guy cannot do this by themselves and would need the help of a professional. Any aspect of safeguarding my seed phrase that would mean exposing it to someone else (who in this case would handle the engraving) is a big risk and one I would not be willing to take.
I personally cannot see any pros to this.
You couldn't be more right. In a similar post about holding your private keys and SP where I once read people suggesting saving this information in a Nuclear type king of Vault, even then I thought that was overboard. As you suggested, "Paper and ink have proven to be effective means" and I also believe that the best way to protect your crypto assets is for you not to even let people know you have them. I believe that we are overthinking this whole login info thing.
'