With a zero balance, identity. Identity is simply connecting to a wallet and reading a signed DID - the wallet could have zero balance and it still works. Boom you just signed into something without Google / Facebook / Apple.
With close to a zero balance (but not quite zero) to pay transaction fees, you can do peer to peer encrypted messaging without central arbiters.
With close to a zero balance (but not quite zero) to pay transaction fees, you can send vast quantities of stablecoins to the otherside of the world - that said a web3 skeptic may consider stablecoins to be a cryptocurrency (there's arguments either way, they're tokens but not minted via proof of stake) and capitalisation is an issue.
Edit: reply to peoplefromibiza, who made some good points, due to rate limit:
> wallets are a cryptocurrency concept
yes, agreed. But they do a lot more than let you speculate on cryptocurrencies. Right now I'm working on wallet for people who have zero interest in speculating on cryptocurrencies.
> you can do the same thing with a client certificate
yes agreed. You can think of web3 as a better PKI. I do.