Doesn't that defeat the whole purpose of cryptocurrencies though? After all this authority could selectively blacklist some coins from ever being converted back to their peg currency, effectively rendering them worthless, couldn't they? You couldn't easily launder it away because this authority could decide that if these coins are used in any transaction then the "bad" coins would contaminate the outputs proportionally to their amount in the inputs, so it would mean that people would double check their inputs not to get "bad" money. So it would be effectively like trying to spend fake dollar bills (except that the authenticity verification would be quick, automatic and completely impossible to fake).

That means that on top of trusting the authority to fairly issue the coin you also give it the power to effectively censor transactions.