How safe is BitcoinCore since it is using owner's passphrase?
No, not all passphrases are used to generate the private keys for a wallet. Only specifically brain wallets do that.
Passphrases in actual wallet software like Bitcoin Core and Electrum are used to encrypt the wallet. The private keys are still randomly and securely generated. Your passphrase is only used as an encryption key so that the private keys are stored encrypted on disk.
It is safe and recommended that you encrypt your wallet with a passphrase. If you choose to not encrypt your wallet, then the private keys will be stored unencrypted on disk and any person or malware with access to your computer can steal your private keys and thus your Bitcoin.