The Signal Protocol somewhat excessively provides forward secrecy for each and every message sent. That is sort of pointless while the messages still exist on the screen. Most people would be happy getting rid of their old messages every week or so. You could totally do that in an instant messaging system that used OpenPGP formatted messages. The reason that no one bothers is because few people want to dump their old encrypted emails. No one wants to dump their old encrypted files. Instead they take advantage of the greater security inherent in an offline encryption system and avoid getting their keys leaked in the first place.
If you really wanted to do message by message forward secrecy using a hash ratchet using OpenPGP formatted messages you could do that too. There is nothing magical about the Signal Protocol for stuff like that...
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