Let's say I have 100 of Token "A" and of Token "B". The 100 "A" tokens are on this private network and Token "B" is on Ethereum. Now let's say Token "B" had a connection to an illegal trade, the user that had traces to Token "B" could be found. If you believe you are safe while using Ethereum please read this article by Decrypt, "https://decrypt.co/19423/we-tracked-133000-ethereum-names-and-exposed-their-secrets". Now let's say Token "A" had a connection to an illegal trade, well on the private network no one would know as it would be private, duh.
AFAIK, decentralized cryptos are more often be public with their transactions, even the centralized ones as well. Publicity of transactions is what the idea of the blockchain is, where you can see how and when the blocks move and how much amount it transacted. But why would someone make a private-crypto? it would give a less trust as the publicity makes a crypto transaction much easier to safe guard, and with such privacy, there would be no chance that a scammed person would even know where the hell is the transaction or if ever the amount were still pending or not.