I don't know why I am only finding out about them now... But a platform that does just this exists already 🙈
They are called "Money On Chain" (okay bad name, terrible SEO, for one thing) and they have a stable coin (pegged to US Dollars) that is called "Dollar On Chain" (short: DOC).
To run their smart contracts they use RSK (formerly Rootstock) and you can "mint" your own DOC by first staking BTC into RBTC and then sending the RBTC to the MOC/DOC contract...