Why do you need stability? The higher it goes the better it is for the users. I hope it goes to $1 million if someone is willing to buy it for that much.
Better for the users, but useless for merchants which have time-shifted expenses - and as long as it is useless for merchants in big scale it is useless as a currency.
Example: (when 1 BTC = 1000$)
Merchant buys goods for 500$ (=0.5 BTC) per piece. Sells it for 1 BTC per piece. (0.5 BTC profit = 500$)
2 weeks later 1 BTC = 1500 $ (aprox. for the sake of simplicity)
Another merchant buys the same good for 500$ - which now is only 0.3 BTC - so THIS merchant can sell the product for 0.6 BTC to have the same profit.
The first merchant need to drop the price to 0.6 BTC (cause of competition), leaving him with just 0.1 BTC profit
You see the problem? And there is ALWAYS fiat-currency involved