If the "wallet seed keywords phrase" is all that's needed to restore a hardware Bitcoin wallet, isn't backing that up a nightmare security-wise?

You're misunderstanding the purpose of a hardware wallet. So first, when you transact Bitcoin without a hardware wallet on a computer, there is a concern that any potential malware on the computer you're using will be able to steal the key (and therefore its associated Bitcoins) because the key has to be stored on the computer.

The point of a hardware wallet is to make it so you can safely transact with Bitcoin on a regular computer without compromising the security of your private key by storing it on your computer. Because the private key never touches your computer, any potential malware wouldn't be able to gain access to your Bitcoin. (So, if you store your seed phrase on your computer, you've entirely defeated the purpose of using a hardware wallet... so if that's what you're doing, I would recommend creating a new wallet and moving the coins over if you still want the security of the hardware wallet.)

If your concern is someone stealing your backed up seed phrase, it is your job to separately protect that seed phrase, whether it's by encrypting it, storing it in a secured location, etc. But these would be done with different tools (an encryption tool, a physical safe, etc.)

You're not supposed to store it in a passwords.txt file on your PC. Doing so defeats the purpose of having a hardware wallet.

As for the handwritten copy the mnemonic is there because most people don't get hacked but instead lose coins due to inadequate backups.

Hardware wallets are designed to protect you from online threats i.e. hackers and malware. If you feel you are under threat in the real world then you need to hire security guards.