Bitcoin is experiencing an incredible bull market, and anyone who has ever purchased this asset is now profitable. If its price stays stable, then it loses the incentive for everyone to chase it. The excitement and thrill that comes with virtual currency is unmatched by stable currencies these days, and the control of the big boys will cause bitcoin to go through the roof. 
That's for sure, bitcoin attracts people thanks to its volatility, I don't believe people will continue to chase it if it becomes stable. The majority of investors come to the market with the intention of making a profit, but once the market does not satisfy the needs of the investors, they leave. I never thought bitcoin would become stable, would be really disappointed if one-day bitcoin stabilizes. Bitcoin becoming stable will not bring us any benefit.