I think if the bitcoin is getting a stable price i do not think there are allot of people will be interested into the bitcoin because they can not invest into the bitcoin anymore because of the stable value they cant get profit so they stop investing off course.
bitcoin is two things: a currency and an investment. if the price becomes more stable then people would use it more as a currency so that would be another way of being more popular in a way. and that is something which is happening the volatility is reducing over time as bitcoin becomes more popular and being used more.