I see two distinct types of coin referred to as "stable coin" -- dynamic supply coins like Bancor, and fiat-backed tokens like Tether allegedly is.
I think there are fundamental problems with Schellingcoins / other smart-contract-based coins which try to dynamically adjust the supply to maintain a peg; the underlying economics seems pretty shaky (e.g. see http://hackingdistributed.com/2017/06/19/bancor-is-flawed/).
I don't think that the same problems exist with fiat-backed coins though, IFF the full reserve is held. The problem with pegs is when you don't have enough reserve to prevent the peg being broken.
Tether is supposed to be full backed like this, but the fact that they broke up with their auditor suggests that they are not being honest about their reserves.
Although, if your USD-coin is issued by Bank of America, and they apply the same fractional reserve rules that they do to their normal deposits, is there any difference at all?
There's nothing in principle preventing a blockchain from tying wallets to KYC'd individuals, thus resolving the UBO for a given payment/settlement; Stellar and Ripple both have KYC protocols built in.