It wouldn't be hard for someone to resell SIMs (even pre-activated SIMs for a premium) to have less data on you recorded at time of said secondary transaction?
But the reseller still has to have their ID on file so they will constantly get deposed in cases where a sim card they sold was used and now the police are trying to identify the buyer. It would be a huge pain for them and I don't see it actually protecting the buyer much.