WETH is short for “wrapped Ether”. It’s a token issued on the Ethereum blockchain. This token conforms to the so-called ERC-20 standard, which is — essentially — the API of the token. Ether itself does not conform to the ERC-20 standard, which is why wrapping it is necessary to e.g. exchange it for other ERC-20 tokens via a smart contract designed for this purpose (confusingly called a “swap”).

WETH is the ERC20(coins) version of ETH. It turns ETH into coins, so the contracts have an easier time interact with it

AFAIK it's the same in the US (the US mint is in charge of both producing and destroying money), because treasuries want to keep track of the physical money supply.

> Why would you ever want to “shred the check”?

You don't, and it's not what technically happens, but it's the closest I could find as the actual behaviour can not be replicated in the real world.

The actual behaviour, at least in my understanding, is that the bank check goes in a box to which only the ATM has access, but the ATM was never coded to look for bank checks in the box, and it's not possible to update it, so it's not possible to get the bank checks out of the box.

In the real world you could take the box out and force it open, but in "the blockchain" the contract has sole control of the wallet, an updated version of the contract would be a different contract with a different address.

> Is this the intended functionality or a bug?

It is, in the broadest sense, a bug: the contract was not coded to handle anything other than ETH inputs, so it ignores everything else, but the other things were still moved into the box.