I think what you mean is 'stable next to some other asset'. Like USD.
Ok, but if they are marked to USD, and you want them to be marked to USD, you have to do a lot of manipulation to keep them well marked ... it's basically an extension of USD! You are amplifying the power of fiat!
But if you don't want to be 'tied' to USD, well, who is going to sell their goods in USD, and then constantly be re-pricing in BTC? Nobody. The answer at the corner store is: "if you want to use BTC to buy milk then convert them to USD first and buy the dam milk".
Businesses in Canada used to keep USD on hand for USD visitors just as a matter of pragmatism, because cash is a pain, but if you can flip back and forth now without a lot of transaction cost, then we don't need that.
So there's no point really in using BTC as a 'currency' because everyone is going to rationally adopt the currency of the local economy for purposes of 'stability'.
If they don't want to hold dollars, then put their money in a choice of other assets.
When they need to interact with another economy, they need the currency for that economy and so they need to trade for those foreign dollars.
There's just no way around it and I don't think that BTC has any role to play in it.