And that central entity is able to say which coins they consider to be legitimate and can be redeemed and which are not. So that seriously affects the fungibility of it all.
Fungibility is always under threat when it comes to exchanges. They're trusted intermediaries; they can censor and steal your money. This is what Bitcoin taught us.
It's not like you can freely withdraw BTC from Dream Market into your Coinbase account. That's asking for trouble.
I think centralized stablecoins are just a logical extension of the already existing exchange ecosystem. When you hold USD on Coinbase, that money can easily be confiscated. Coinbase can just freeze your account and reduce your USD balance to zero -- and then maybe pass your information onto law enforcement. Why would exchange-issued stablecoins be any different -- because they're "crypto?" They're still just centralized IOUs from an exchange.