Nope if it had a stable price then you can't use it as an investment for example if all the stocks had a stable price then why would people simply invest. Bitcoin is an investment platform so have a stable investment won't attract anyone. And i don't think in the next 10 years the price will come down to 0.1$ or 1$. If it was stable then it would be perfect as an currency but the current status of bitcoin it isn't stable at all.
And people will just use fiat if bitcoin has a stable price. That's why I believe that bitcoin is not going to be popular if it has a stable price. And I guess it is better to say that bitcoin would still be popular if it has a flooring price. Because there are people who are defining floor price as stable price but that is different for those folks out there.
No that is not right because if the price of bitcoin will be stable then it will not mean that people will leave it but people will then store their money in bitcoin and will keep that money for longer because most people do not believe on banks and they want to search for another source of money saving which they want to be not in any third party control.