Not really true that it depends on the government. And even if it is, you only need like one government supporting it for it to be valuable.
Why couldn’t your argument be used to say the internet won’t work?
This is true! But databases don't have that magic "blockchain" tech.
David Gerard's book Attack of the 50 Foot Blockchain touches on the ridiculousness of this idea, actually. And, yes, it's ridiculousness, but it's what some people are trying to sell.
So should I take it that you're one of the people who thinks blockchains have little applications outside of currency?
If you can find some other reason for processing transactions and can guarantee that the population is big enough then the coin becomes unnecessary.
An extrinsic reward doesn't have to be financial though, it's anything that you want to get out of an activity that isn't part of the activity itself.
If the blockchain ledger was a part of a greater whole and the client software of which it forms a part was somehow intrinsically fun, useful or needed, the token itself wouldn't be necessary.