There is a second advantage of a key file, separate from simulating two-factor authentication (2FA). Although your revision of your question suggests that the two factor answer is what you are looking for in your answer.
Another reason to not have the encryption key be derived directly from the Master Password is to allow the key to be created at random instead of being directly derived from the master password. If we create the key with a CSPRNG and then encrypt that key with a Key Encryption Key (KEK), then we can ensure that the master key has the full strength of its bit size. That is a 128 bit key will really be 128 bits strong, even if an individual picks a poor master password.
Although this isn't required for symmetrical keys (as used in password managers), it is absolutely vital when looking at public key systems. In those cases the private key can't just be anything, and so can't really be a function of a password and some salt. So this is why for things like PGP or SSH the keys are generated by the software and are then encrypted with a KEK derived from the password.
Of course the derivation of the KEK from the master password still needs to be "stretched" with a key derivation function such as PBKDF2 or scrypt.
Two factors, but not authentication
Note: The reason I said "simulate two factor authentication" is because there is actually no authentication in these cases. Instead there is decryption. For many purposes, the distinction doesn't matter, but there are crucial cases where distinguishing between an authentication password (or token) from an encryption token is enormous.
In the case of something like KeePass, which are not authentication based (You are not proving who you are to some service which then releases stuff to you upon success), you need to get your key file to every computer or device you need to use your data on. So putting it on a USB-thing may not work if you also wish to decrypt your data on a phone. There may very well be ways to do this with KeePass, but given my (possibly flawed) understanding of the architecture it would present some difficulties that would need to be overcome.