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I think it might just be that, while they want the app to be used, its not meant for general consumption yet.

So publishing only the apk selects those users who can tolerate semi-broken software.

Or Google Play could provide a 'beta' channel for publishers. Does such a thing exist?

Yes, we use the same for our app. You need just to link a google group or a g+ community in the developer dashboards. It works quite well.