They will certainly continue to exist

I will tell even more than that. With prices rising we should in fact expect even more fluctuations and higher volatility. But that's not my point. That said, I still heavily disagree that with stable prices Bitcoin will be less popular. First, this is an impossible thing on its own, as it is with any mostly financial (read speculative) asset (due to its virtual nature). But even if we could think up or contrive some invisible mechanism (Dextera Domini) that would keep Bitcoin prices bridled, short term investors (read speculators and profiteers) would certainly leave but they will be quickly replaced by long term investors interested exactly in that, i.e. in stability of prices. Gold is losing in dollar terms (i.e. dollar inflation outperforms gold prices) but does it lose its popularity, shine and appeal?