Encrypt symmetric session key with asymmetric or symmetric master key? Every day, I must backup my server's files, encrypt the backup, and upload it to untrusted cloud storage (dropbox, s3, etc.)

I've spent time on security.stackexchange where I discovered the typical approach is:


encrypt the backup with random one-time symmetric key ("session" key), for speed
encrypt the session key with an asymmetric key ("master" key: the public key in a public/private keypair)
upload the encrypted backup and encrypted session key to cloud storage


But I don't understand: why not use another symmetric key as the master key? Put another way: there is no key exchange here, as I am both "sender" and "receiver" - so how do I benefit from using an asymmetric key as master?

(For example, I'm using gpg, so my server could store a symmetric key with a 100-char passphrase, and use it to encrypt the daily session keys.)
Symmetric cryptography could well work here, to be honest.



The main advantage of public cryptography in this setting is that you can encrypt by just using a public key. So you'd get the following operations:

Setup:


create public / private key pair;
encrypt private key with password.


Encryption:


create random session key;
encrypt session key using public key;
encrypt data with session key and random nonce.


For decryption:


decrypt password-encrypted private key;
decrypt session key using private key;
decrypt data with session key using random nonce.


In other words, during encryption you  don't need access to the private key and therefore you don't need a password either. You just need to make sure that you don't leak your temporary session key.

This seems to be particularly useful for backups where backing up is frequent and commonly automated, while the restoration is commonly manual and infrequent.



Notes:


the private key may also be otherwise protected, e.g. stored on a USB-stick or generated within a smart card (exporting the public key after key pair generation);
instead of deriving a key per session you might also want to generate a symmetric key per file - beware that some modes such as GCM have clear restrictions about the amount of data that can be processed by one key;
restoration is often too infrequent, don't forget to test your restoration initially and frequently thereafter.