I don't think that cryptocurrency are better than regular currency simply because cryptocurrency don't work offline. Transaction in cryptocurrency charge very high fees and require some time to process and confirm m. On the other hand, regular currency can be exchanged quickly without a fuss.
That's the worst argument I've heard against cryptos.
Transaction fees are a problem, yes. But they are still relatively low. You're only paying $2 per transaciton approximately right now, not ideal but still quite manageable in general. I know that in the past you were able to pay just a few cents in transation fees and still get your transactions confirmed within the first block or two, but $2 isn't that bad still if you are sending overseas to your family/friends compared to all the fees and charges added up on paypal or perfectmoney.
Cryptos don't work offline, yes. That's a disadvantage. But the advantages of using crypto(decentralization, store of value etc.) far outweigh this disadvantage. Most people's got internet connection anyways even in developing countries like India and China. If not, there are services that you can send SMS's to to send bitcoin transactions. I think you forget the fact that regular currencies are strongly based on the internet as well. Internet banking is what most people use nowadays anyways.