Doing it right is exactly the thing that makes this impossible. If instead you give everyone a unique barcode that every other pseudonym can be tied back to, do you really think that database will never be breached? It would become the prime target for all attackers in the world.

Meanwhile reconstructing "identities" is the least valuable thing to doing law enforcement well, because the first thing criminals will do is use someone else's identity, and then tying something to the wrong identity isn't just useless, it's actively counterproductive. The thing you need is not centralized identity but proper investigations that can tie some activity to the person pulling the strings regardless of whose name they're using.

The thing centralized identity does is precisely the opposite -- it leads you to person associated with a name, often the wrong person. You want to get the person offering to do murder for hire to think they have a contract and show up somewhere you can arrest them regardless of whether you know their name, not to convict the person whose identity they stole.