Do you think if BTC had a stable price which could only be altered by $0.01-0.10 it would still be as popular and as used?
In my opinion it will be more popular. Having a stable price will welcome investors that doesn't to take the risk into investing to bitcoin because it is volatile. As an investor ofcourse you will go as possible with something that is less risky to have an assure profit. And if Bitcoin will be less volatile, it will catch the attention of more people and will make it more popular.
If you ask me, if bitcoin had stable prices, it wouldn't have been able to touch its current value. Moreover, if the prices become stable even now, people will take it as an asset like gold. Volatility has attracted many people but still the fluctuation should not be at this much rate as it is now. It causes panic among users.