Having to create issues-only repositories seems like a sign that one may be using the wrong tool. But the simplicity of GitHub Issues, and the fact that most issues on my plate are related to a particular repo, makes it tempting.
JIRA is a pile of bolted-on features, and no one has ever measured what is essential to project management, so this point strikes me as sort of an ad populum than an argument that JIRA or whatever is more fit for some PM task than Github Issues.
This is what kills me about software project management, at least in Enterprise where I work: its about people consistently communicating to one another; that's it, lest there's something else we can extract as somehow more primordial. Somehow people consistently communicating over a topic has been reified to the point that we mistake the reified things for the thing-in-itself.
My gig is still in Trello-land and I'd like to move away from it but companies have a tendency to include biz folks in Trello whereas Github is scary tech world to a lot of them.
I understand they want to get it "right" before opening up to the majority, but project management isn't something a business can sit and wait. People have to use some other tool in the mean time, and once having invested time and effort they won't switch back easily.
Generically, we're talking "Kanban board" with swimlanes for the status, tags for categorization, and comments/attachments for discussion tracking.
I'm currently in a position to get some people sync'ed on projects for a client, and I am going to recommend we use Trello.
Kanban is just the right level of organization and visibility without going full agile-daily-standup-sprint overload.
Use it to track white papers, project planning documents, a project-wide wiki, et c., if you want to feel like it's for more than just issues. Though having an issues-only project doesn't seem worse to me than using any other stand-alone issue tracker, separate from GH.
I drop a single README.md in the root of the repo that links to the issues and leave it at that.