quickref is another tool which tries to publish documentation extracted from packages, but quickref would
like to skip packages which are not part of the public API, such as test case packages which may require
other non-public testing frameworks.

I'm not sure that ASDF can do anything about this one -- packages are not an artifact that it really understands or takes responsibility for. Perhaps it would be better to extend the package object so that it can hold a slot that can designate it as internal or external. Quicker could provide a trivial system that would export this package extension. I think it would be useful for other documentation systems, as well.