Take it from someone who has gone down that path, it's a support nightmare, especially when you want to allow cross-device sync. Much easier to just require the account up-front.
It may be easier from the engineering perspective, but its a major turn off for the user. Building good user experiences is often harder than the engineering part.
Overcast has a web client, too. If Overcast used the UUID, it wouldn't be able to give you the web client side of things easily.
You can't get a device UUID anymore I don't think.