is there a service that pegs BTC to fiat and backs it with BTC?

[riclas]

I know a lot of services that peg BTC to fiat and keep reserves of the corresponding fiat to maintain the peg (abra, tether, coinapult, uphold, bitshares).

However, all of these still require those fiat reserves, and therefore the peg may not be honored if the service is gone. Besides, these reserves force these services to ask their customers for KYC and AML compliance.

Is anyone aware of a service that backs up a fiat peg with Bitcoin itself?
I can imagine this being done with smart contracts and CFDs. On the clients side, it would allow them to hold Bitcoin worth approximately the peg value in the worse case that the service disappears.
Does anyone see potential problems in such a service?