You're forgetting the revenue from the Xbox Marketplace.
Isn't that revenue completely dependent on Xbox install base? I would wager that 95+% of their revenue comes from console software.
What is another service-based metric that makes more sense than number of users? What other primary (read: most important) metric do you assign to the Head of Xbox that signals he's doing his job to attract more gaming users to the broader Windows 10 platform? I'm seriously asking, because it seems you know something I don't and I'm eager to learn.
Revenue. That is a very relevant service based metric: how much money you are extracting from your customers.
What secondary metrics should one track, then? Number of active users and ARPPU (average revenue per paying user), at least. These are things you can try to influence with pricing and offering, but also by making the service available to people. Microsoft can make Xbox service available by selling Xbox consoles or by activating them on Windows platform.
Now, here's a tricky thing: you cannot only measure people who have access to your service, you also have to understand stickyness. Xbox console owners are far more likely to spend money on your service than people who have an Xbox application on their mobile phones or Windows PC (NB: this is purely my own assumption). Therefore an "active Xbox Live user" is not a meaningful concept in and of itself, because the ARPPU of a console owner can be upwards of $10/month, whereas on Windows and mobile it may struggle to reach $1.
So, the install base (and hardware shipments) of Xbox are an extremely relevant metric, when it comes to understanding the revenue potential of the service.
IMHO.
Why not go completely 3rd party then if hardware is such a drain that this would be a win?
Strategically, this would make sense. MS is a software company at its core, and the profit margins are much higher on software than hardware. Given that their cost of capital must be pretty high (they do pay generous dividends, don't they?), I'm surprised that they can afford an expensive undertaking such as Xbox.