I think it won't stabilize, but the movement of price will slowly move from some timeframe. What I'm looking forward to is the benefits we could get in the future; locals will show more interest as we see multiple platforms adopting bitcoin; of course, demands will be high so opportunities for holders will increase. Maybe there could be better alternatives in the future, but it won't happen very soon.
The initial concept of cryptocurrencies is decentralization so it will never be stable, of course there are benefits when the price is unstable because it gives profits when it goes up and can buy at a cheaper price when the market goes down, maybe when the market cap has reached 100x from now the price is more stable because it is impossible to exist a person or company that has the power of money to control prices.