Additionally: can you make cryptocurrency transactions offline? In my opinion that is a crucial part of the "digital cash" idea. I don't know the technical details so it would be nice if someone more knowledgeable could answer.

I'll even throw in a scenario that I've encountered: the card readers in a store aren't working, because there is a connection issue. Instead of using cash in my literal physical wallet, I'd like to pay with my digital wallet. Can I conduct my transaction offline with the store?

You can do an offline transaction, but there's no way to prevent double spend until it's online. If you gave some crypto to someone offline, you could double spend it until the recipient is online and publishes the transaction.

AFAIK, the blockchain is online, so I can't conceive of a way for an offline transaction. I suppose you could write down your wallet service and/or ID on a piece of paper, then when the store goes back online they trustfully transfer the digital money, but even then one of the parties must be online.

My perspective: I don’t see bitcoin replacing fiat anytime soon, so for day-to-day transactions, cash works all good! No need to replace it completely. They can coexist.

In the scenario you mention, I’d just reach for cash.

However, as a protocol for payments/value in the digital world, it’s very compelling.

If we are aiming to re-think currencies and use cryptocurrencies as the new building block, I feel like it should handle these cases, otherwise we will need to re-do the whole thing again in the future. I'm too lazy to do this multiple times.

Then you can use Bitcoin Lightning, a micropayments network layered on top of Bitcoin, and settled on-chain. There are solutions to these things, it's still just an early market.

Oh yeah, that technological marvel/crutch when every single participant must lock permanently a big sums of tokens in advance to each other, and then the system will solve that little easy CS problem called "traveling salesman" in realtime on millions of paths and clients simultaneously. That one? Amazing and really enticing proposal but I'll stick with predatory mastecard for now, tyvm.