Private key

I have a question about the private key that my passphrase generates. I understand that the private key has a complementary role along with the public key in performing the transaction. But I don't understand why it's important to write down your private key. And we never write it personally during when we are performing transaction anyway. The software does it for us. Isn’t it more important to know your passphrase and regular backup wallet. dat file. Does the private key serve us to restore the wallet? Is it not possible to do this via the passphrase and wallet.dat file? If someone somehow gets my private key, how exactly will it help me that I have my private key written down somewhere.

I'm a layman, I'm just starting to learn about cryptocurrencies. Sorry if my question is stupid. I am sure i do not understand something right.