That protects your seed phrase backup in case someone get their hands on it.
Even with the seed phrase, they still wont be able to restore the correct wallet without the passphrase.
On the other hand, your Electrum wallet's security will not be directly affected by that passphrase since it already contains the derived master private key from the seed phrase and passphrase.
On the other hand, your Electrum wallet's security will not be directly affected by the passphrase that you set since it already contains the derived master private key from the seed phrase and passphrase.
It's your machine's security and other factors that'll dictate if your keys will be safe. (e.g. 2fa or cold-storage)

So do it if you think that the location where you'll save it isn't your safest option, not for "increased security" of the client.

That protects your seed phrase backup in case someone get their hands on it.

On the other hand, your Electrum wallet's security will not be directly affected by that passphrase since it already contains the derived master private key from the seed phrase and passphrase.
It's your machine's security and other factors that'll dictate if your keys will be safe. (e.g. 2fa or cold-storage)

So do it if you think that the location where you'll save it isn't your safest option, not for "increased security" of the client.