Exactly, except I don't see why do you think it's a narrow case? Legal ways are burdensome, expensive for those who can live a week for $10, and sometimes don't work altogether because of political reasons which are unlikely to disappear soon (I don't even sure they have to disappear at all). And economic migration is huge, so it's safe guess to say that number of people who need to send money back to home country is very significant. And now it's already being done via gray, and illegal schemes, in fact. (Please note: "illegal" is used as morally neutral term here because laws could be wrong, or simply inefficient.) In many places around the world you can find a sort of alternative banking in a medieval fashion - as a trusted network of individuals, and families. One may expect regular online bank should beat this system, but it just doesn't happen, because of reasons I mentioned.
Somalia remains politically disintegrated by warring factions which I think is a bigger factor then currency rates and still there's internet, that's what I'm saying. Also, myself lived in a country where price of local currency could substantially change during a day, and it wasn't the end of the world. In those times much fewer people used internet, but it was there, electricity was there, no zombies walking in streets, shops worked, and rule of law (even if bad law, and bad rule) remained in reasonable amount. People just started to ignore that part which prohibits use of foreign currencies. Payments were often technically illegal - you see the pattern. Would I use bitcoin then if internet were as available as it is now? I can't say for sure, but maybe. Depends on circumstances like taxes, enforcement of currency controls, availability of US$ cash, need to make cross-border transfers.
Don't know a lot about Venezuela's current condition, but if electricity has become luxury already, an intermediary can solve this trouble, it could still be more efficient than moving cash in bags.
Yes, the international transfer system isn't great. But that doesn't mean that blockchains are the best solution. Or a solution at all.
Is Somalia undergoing economic breakdown? I didn't find much evidence for that, and war doesn't mean that it is. And if it isn't, then it's not the kind of economic-collapse case that is typically used to justify Bitcoin.
If you're using an intermediary, then there's no real point to a blockchain solution. Blockchains create a trustless context. If I'm willing to trust an intermediary, then a blockchain doesn't add value.
I don't think high inflation on its own destroys access. I think a failing economic system definitely harms it, just as it harms every other business activity. Last I heard, if you were going to run your own Bitcoin node, you needed reliable connectivity and power. Try doing that in Venezuela right now, where people are barely getting food, and where the government has cracked down on people getting around its financial controls. (Somalia's a bad example; inflation there is reasonably stable now.)
And if you're not going to run your own Bitcoin node, but instead are using a service, then there's really no point to having a blockchain. At that point, you are just using a bank with a highly volatile currency and an overcomplicated transaction database. You'd be better off using a regular online bank and some stable currency.