Once you can have a single BAT wallet that is used by all your devices (another feature that I assume is in the works), it will make a bit more sense to buy BAT with dollars (instead of with ad views).
If you're making that purchase, you might as well time it with a down-swing in the price (or away from an up-swing). Some users will spend more cycles on timing their buys than others, and those users will have a stabilizing effect on the price.
Also, the price of BAT in USD over the last 60 days has stayed between 0.12 and 0.24... it's not exactly as crazy as you're making it out to be.
This is just pushing the problem one step removed.
Is it not only relevant what you trade for your groceries?
If you can find someone to take BAT for that, in stable exchange rates, then your point stands.
If you have to acquire $ then what the exchange rate is for $ to BAT comes back into relevance.
Again, perpetually trading BAT back and forth for showing ads/watching ads is restating my premise about holding BAT.
Whether people will be willing to do so greatly depends on exchange rates and volatility.