I have seen from different sources that the sole purpose of the master key should really be to generate the subkeys, and that it should be subsequently backed up to an offline location and deleted from the device on which it was generated. Why is that? I just don't get the rationale for having both master and subkeys since, ultimately, they're all associated with the same passphrase.
The primary key, and only the primary key is allowed to perform key management operations (adding and removing user IDs, subkeys, ...) and issue certifications on other keys. Storing the secret primary key offline provides additional security against misuse of those especially sensitive operations.
Furthermore, the primary key is target of incoming certifications from other keys. If you have to revoke a subkey because it got compromised (computer got hacked, issues like the DSA and random number generator bug Debian had), you roll over your subkey and everything's fine (at least, for messages encrypted/signed in future). All your contacts have to do is fetching the updated key from the keyservers running
gpg --recv-keys <key-id>. If you have to revoke your primary key instead, you lose all certifications on that key: all trust in that key is lost, you will have to start over distributing your key and getting it signed.