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?
I do not think that bitcoin will be more stable, because it is not regulated by anyone and depends only on user activity.
Are you suppose to say that it is not going to become popular if it has a stable price? This is why bitcoin is being liked by a lot of investors and other people that are pushing decentralization that wants to avoid taxes from the governments and wanting to have an anonymous transaction. And the price is unstable which is giving more chances to make profit.
Popularity of bitcoin is depending on the situation, if more and more stores and malls like bitcoin for being stable then it will continue to become popular because it will have a fixed value just like in the fiat but a lot of advantage while it can be popular also if the bitcoin price is unstable because a lot of traders and investors will also like it and it will result for bitcoin to continue becoming a popular currency.