Right, but the transaction that turns Bitcoin into another currency is traceable because someone needs to claim that currency, either via ETF into a bank account or physically going to pick it up.

Absolutely, and for Bitcoin that's a big problem for a thief. But for a private currency like ZCash or Monero, nobody can tell where the coins came from. They can't prove you stole them.

E.g. with one scheme, you destroy your coins and get a proof that you destroyed them. Later you can submit your proof to the blockchain and get new coins minted for you. But it's provably impossible to for anyone to figure out which coins you destroyed.

You could just spend them at a legitimate business though.

How do you redeem your goods and services without somehow tying it to yourself? For example, physical goods need to be shipped somewhere. There seems to be a limited number of things that you can spend your cypto-currency on that would not somehow be traceable back to an actual person, no?