My main feature request (and I'm not sure if any competitor does this, so please inform me if it exists somewhere):
While Paw allows me to export code, which is cool and all, it would be very interesting to allow me to compose workflows, like, say Automator in macOS, including assertions, so that I could essentially compose and export integration tests with Paw. It'd be neat to see some more generally API-definition features hit Paw, or maybe a companion app that plays nicely with Paw to do the definition half of things, compatible with Swagger and whatnot.
Clearly not a well-thought-out idea, but I think there's space in Paw's domain for some form of what I'm talking about.