Yes it will probably be like gold in digital form but I'm not sure it will happen because bitcoin is decentral and bitcoin holders will not get much profit, I like the fluctuating bitcoin
It wont be happening anytime soon considering the importance as a trading commodity in people's minds. Many traders are thriving on the fluctuation in prices, making daily profits there and thus leveraging the market even more. That drives the economy and the price of bitcoin considering a local currency. If it get stagnant then traders are likely to sell some coins - while others will buy it - so the stagnancy will be temporary and not permanent.
Now, people have different opinions on what I'm about to say, but having volatility is a very important part of the market for Bitcoin, or at least it used to be. Not sure if it has that much of an impact anymore. Something that really drew early investors in was the ability to make a lot off of the swings so prevalent in the market, nowadays I don't know if investors care all that much. I think everyone is just looking for growth.