Apps that naturally depend on the Internet can use a model I term as “free with subscription” or freesub. In this model, the app itself is free to download with some features available from the outset. Other features are enabled based on subscriptions or credits purchased over the Internet. An example that comes to mind is the Skype app. The landline calling feature is only available when you are a subscriber, or purchase additional credit using the desktop app or the Internet browser.
This may be one means of circumventing the App/Play/Windows Store cut. I wonder if the stores have specific terms that prohibit this. I am aware that the apps themselves cannot accept payments directly.