Why couldn't a privacy focus coined, like Monero, be a stablecoin?
You don't need to see where the coins are and move to promise $1 of going for every coin.
How are you guaranteeing that your private stablecoin will keep its $1 value?
How are you bootstrapping a network to validate private transactions without the promise of potential gains in coin value as its popularity takes off?
Who makes that promise? That's who you are ultimately trusting.
Probably the founders/employees of the company issuing/redeeming the token would be arrested very quickly. Tornado Cash people got arrested for much less.