Price stability is very important for the adoption of bitcoin. When the volatility is the same as US dollar, more people will use it.
But in reality only after getting a higher adoption the volatility in price goes similar to the dollar or other currency. So initially people need to believe in its potential and adopt to experience stabilized value for long run.
If there are more holders and investors, it will be too hard for market markers to play with the price like they are doing now and have been doing for a long time. So this kind or increases eventually will come to an end.
This is not sure. Just look at some large companies. Their stock is also very volatile so there is no guarantee that the price will be volatile.
I do think though it will be less volatile if it is more mainstream.