There are better ways to have both privacy and a simple way to audit the supply like Bitcoin.

My idea of a privacy coin would work something like this:

1. Have a network of relay nodes constantly running symmetric data streams for uniformity, randomly routing data through the network in broken-up chunks

2. Have every minimum unit of the currency (every "Satoshi" equivalent) be its own keypair. When a user signs a transaction, it tells the network to generate new keypairs for each one in the transaction and give the recipient the new private keys

3. The public can see the pubkeys for every unit of the currency, but can't see which ones were and weren't transacted together in each block, because of each node in the network transmitting data in separate split-up chunks along random paths