Bitcoin can be tracked and a government could mandate that the bitcoins you use to buy a house be from the "legitimate" subset of bitcoins. With Monero, you can earn money from selling weed and turn around and buy a car with the exact same coins. Nobody can even ask you to prove where they came from, short of declaring them as income, (as with cash) but that becomes much harder when you can just fly to France, buy a house there (the government doesn't care if you paid taxes for that money in another country), and fly back.

Yes but the private currencies break the linkage between transactions. You turn the currency into something useful, and that's probably traceable to you, but nobody can tell where that currency came from.

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?