Public (Open Membership) Click to Join Prompt

Christopher G. Stanton said:

The problem that's being laid out here is that when participation and creating content is controlled by being a member of a group, it is difficult to make that restriction obvious to users because the buttons for participation are hidden due to permissions.

This is where there is some confusion, content creation in reality is not controlled by membership.  Nor is subscriptions or notifications.   Everything is governed by permissions.

Membership is really just a template of permissions for the group outlining a common set of permissions for specific scenarios, but are highly customizable and frequently change from the default to suit varying scenarios specific to a community.

Christopher G. Stanton said:

It doesn't make sense to purposefully restrict participation using the permissions to only members, only to then decide to change that to every user.

This is just an example of what can be done, but is probably not as unheard of as you might think.  A more common scenario is to do the reverse, to allow membership but further restrict.  So you may have a group where you want people to join but they cannot post, in which case they are still members, but would have no new button.   

Christopher G. Stanton said:

Which is weird, because I would have expected the experience to be to show these things as a 'call to action' and then prompt the user to join the group

While technically possible this is where the idea of forcing membership using the content creation flow does not necessarily work because that creation is not based on membership.  You could end up with a result where the button is clicked, the user joins, and the next thing they receive is an Access denied message. This would end up not improving the experience at all.  

The goal is here is to explain why the content creation controls hide as they do and why the  better solution is as directed, you can customize the theme or the widget to make Join more prominent.