Why? The wallet is a blockchain address, not something on the device. Why do I need a thing to just store BTC?
Discussion
The "wallet" isn't a blockchain address, it is a private key used to sign Bitcoin transactions. A cold storage device stores those keys in a place they can't be easily stolen from, and let's you sign transactions to broadcast to the blockchain
It can't do that without some kind of connection to the internet, so... How does that not just defeat the purpose of the thing?
That's the whole point of a cold wallet 😂 The key is on an external, non internet connected device. You use that to sign the transaction, then transfer the signed transaction back to an internet connected device to broadcast to the blockchain.
But why do I need a device to do that? If I just have the key, I can sign.
You don't need one, but it is probably more secure. A key stored on your computer or phone can be more vulnerable to theft, hacking, malware, etc.
The real answer is you really don’t need a hww/signing device.
You only really need one if you want to make & keep xpub/xpriv completely offline for maximum security.