(updated based on new information received from the GPGTools developers)
What if you want to send an encrypted email to someone, and you know the right public key to use, but their public key does not include a UID with an email address that matches the address you're sending the mail to?
What if you want to turn encryption on by default for an email account, so that you never accidentally send an insecure message?
What if you'd like to open an editor, compose some text, and and save it in encrypted form without ever saving the plaintext to disk?
It depends on which text editor you use. By default the appropriate context menu entries do not show up in all editors.
What if you find a public key you'd like to import posted on a web page, and you'd like to import it into your keyring via the clipboard instead of saving it as a text file first?
If you use the keyboard commands to paste a public key from the clipboard while the key manager has focus it will import the key.
What if you'd like to encrypt a file and make sure that it ends up in ASCII armored format (suitable for sending via an email, IM or forum PM) instead of binary format?
Also possible with manual config file editing from a terminal
defaults write org.gpgtools.GPGServices UseASCIIOutput -bool YES
I don't normally use Apple platforms exactly because of things like this. This software is beautiful, but trying to actually use it for anything serious is an exercise in frustration. There's nothing worse than having a computer simply refuse to do what you need it to do, when you know perfectly well that what you need done is possible.
Edit: In the end, all the tasks I needed to complete are possible with GPGTools, but the means to do them are not always discoverable or intuitive.