Found a bug...
If I add a client, and create a recurring invoice, then subscriptions do not work. Only one-time payment can be made.
If I go through the hassle of making a module (what is that for, anyway?), then create a service, then add a client to the service, only then does it allow subscriptions.
For a custom customer -- let's say somebody that hired you for 3 months of special coding -- you'd have to go through the nuisance of creating all this extra stuff. Furthermore, would it be visible on a front-end via the order form? It's supposed to be a "billing panel". At the base level, it should do at least that, and extra steps should not be needed.