Volatility isn't just up and down. It can be just up.
Now generally I'd agree you don't want massive volatility, but that's a function of its age. A market of 50 thousand users is easy to manipulate by one rich guy. A market by of 1m users is still easy but harder. A large 100m user market is really hard to manipulate. This means volatility should keep dropping as bitcoin grows.
Second, a market where most users are speculators is more volatile than one where most are users. As bitcoin becomes larger it'll only do so on the back of genuine consumer adoption. That, too, causes volatility to drop.
Does practice confirm the theory? Yes. Every single year bitcoin volatility has dropped since inception. It's always trending down. All the talk about volatility isn't so interesting to me as it's a function of its youth.
Play out the end of an asset bubble in your head. Lots of people sell their assets, and now have dollars. The job of our policy makers is to make sure dollars don't increase in value at all, and don't decrease in value too quickly. But if lots of people are exchanging assets for dollars, the demand for dollars makes the value go up. Our policy makers will take a variety of actions to make their value go down by up to 2% a year. If we're lucky, they'll be able to stave off deflation.
So if you've sold your assets and want to store your value, you really want some sort of ledger with a predictable supply so your value can go up, not stay the same or decrease by 2%. Gold is traditional the ledger that people seek when these sorts of things happen. But enough people will choose Bitcoin to raise the price significantly, which will make others choose it as well.
Gold might be the right bet, but Bitcoin is a more functional ledger (easy to store, easy to transfer, etc.), and the upside is higher. But again, maybe I'm crazy.
In particular: the effectiveness of a store of value is based on its ability to retain its value over time. The effectiveness of a speculative asset is based on its users ability to transact based on predictions (up or down) of its future value, regardless of its true value.
Being as how a transaction requires two parties, this is not possible for everyone.