Also, the problem can be solved even more simply and elegantly than sharding by having a multi-cryptocurrency ecosystem which supports fast, decentralized, and low friction conversions exposed via the same (interoperable) transaction APIs. If the on-chain volume is sufficient on all chains, it's possible to automatically determine relative prices of tokens... In the same way that tourists from different countries can spend their native country's currency locally (conversion is not always necessary if the relative prices and volumes are somewhat stable).
If the on-chain transaction volumes of different cryptocurrencies are similar (or above a certain threshold that corresponds to the size of the businesses accepting the cryptocurrency as payment), then a business can effectively accept payment in any cryptocurrency which they know/trust the existence of since the API would be the same across all chains. So you could use the same passphrase to log into all the different chains (including ones you never heard of) and you would already have an account there. You don't need to trust the chains themselves with your passphrase, you only need to trust your wallet app since the passphrase should never be sent over the wire.
Wouldn't it be great if you could just walk up to a local business and offer to pay them in some new cryptocurrency they've never heard of which supports the same API? They could verify whether or not it meets their volume/stability and exposure requirements automatically in a couple of minutes.
We're so close to achieving this ideal. The tech already exists in various forms. We just need regulatory/taxation clarity and a bit of willpower.