You only need to secure the seed phrase. The reason is just security. If you are still confused about securing the seed phrase, there is a post about that.
Wallet mnemonic seed is important for wallet recovery and need to be stored, backed up and secured, but you said one thing wrong.
If you have wallet files on devices, you must secure those devices and those files too because there are two ways of losing your bitcoin.
- Losing your wallet mnemonic seed or private key.
- Losing your device, wallet files and they are accessible by other people.
It is more accurate to say you must secure all of them: wallet mnemonic seed/ private key, wallet file, devices that store your wallets, where you store your wallet backups.