I don't know if stability of Bitcoin price would contribute for it to become more popular but I know that people like Bitcoin because of its volatility. This gives them opportunity to make some money and everyone likes money. I'm not sure that currency like Bitcoin could ever be stable that is just not the part of its nature.
I don't think that Bitcoin volatility is part of its nature
Bitcoin was conceived as a means of payment as well as a payment system in its own right. There is nothing in that which could be construed as volatility built in. The volatility we see today is primarily due to Bitcoin itself being used as a speculative asset for the most part. Its use as a means of payment for real goods and services is still tiny. Wider adoption of Bitcoin by vendors and producers with the reduction in its role as a vehicle for speculation will make volatility subside greatly in due course
Sure it had been created for micro payments, as a currencie, but since the begining Nakamoto made bitcoin to became a speculative currencie, since the halving events had been introduced, soo even if we people didnt force those, it would happen the code has those feature to make bitcoin achieve and grow over time in value, people interest has made bitcoin worth what its worthing, bitcoin could be traded and mined unders 100 dollars if people hasnt invested at it.