If there's Internet outage, I won't have my bank account, communication with some of my friends, I won't be ale to check prices, stocks, news, you name it. I'll have to wait it out and endure,, like most other people. The difference is that I have cash. I have almost the same amount of money in physical form than I have in digital, so I'm sure I'll be better suited to survive than people who rely on their credit cards.
With inflation levels rising sky-high, it would be dumb enough to hoard cash in case of emergencies. You're better off holding Gold or BTC in a paper wallet. The latter can still be used without an Internet connection. It's just that you won't have a way to declare transactions as final (unless you connect to the Internet and broadcast it to the Blockchain). It's something I wouldn't worry much about. Especially when there are many ways to get access to Bitcoin. The only downside is the limited number of merchants accepting the cryptocurrency as payment method.
At least, BTC is off to a good start. With due time, it will improve enough until it becomes a "force to reckon with". Just buy, "hodl", and forget about the rest.
I have the opposite thought, it would be stupid to not have cash or savings. Inflation sounds very terrible and terrible but I want to know what is the annual inflation rate in your country and is it so terrible that it loses 30% of its value in a short period of time? Meanwhile, BTC could even drop 20% or even 50% in a few months if a black swan occurs, and I don't think it's a wise idea to have all of our assets in BTC.
Many people keep talking about inflation but do they really know how much inflation is in their country and what the short-term impact is? I guess not many people know but they love to talk about inflation every day. You should have some cash or some emergency savings because I believe that our cash will not suddenly lose 20%-30% of its value in a month or a few months.
Investing for the long term and saving for emergencies are completely different.