One thing to remember when comparing fiat to cryptocurrencies, is that all currencies
have an agreed upon value placed on them. All of them. You're deluding yourself if you think any currency is stationary in value at any given time or place.
The difference is, fiat is well established and "backed" by a governing entity of some nature. I say "backed", because in all honesty, you really can't know with absolute certainty if the committee(s) overseeing the market value and production is as well informed or well intended as we'd like them to be. Cryptocurrencies, BTC in general - with thanks to the blockchain - is overseen by a network of committees, all working to maintain it. The value is derived solely by the market demand and availability.
It fluctuates drastically because it's still a a very small drop in the pond of the available financial assets on this planet. (Available liquid financial assets somewhere around $90.4 trillion USD, not including investments, derivatives, holdings, etc.) It'd be as "stationary" as any fiat is today if it held a larger pool. Same is true for any currency. The larger the pool, the more "reliable".
The real difference, to me anyways, is that it's verifiable and it doesn't pretend to assume it has a grasp on its own value, unlike fiat. It's value is exactly as the market says it is and can't be influenced otherwise. If a whale decides to play with it, it bubbles up, slams down, then reverts back to where it was a couple of hours or days prior. It's happened so many times that I just laugh every time. (Look at the current value and you'll see what I mean.) Watch it as long as I have and it's an amusing financial experiment of a truly astonishing, first world oriented currency.
The main thing is to ponder the long term goal.