Google does provide updates. It's the device manufacturers and/or mobile operators who choose not to push them.
That is a lie and you know it. Google updates the OS, but they are also directly responsible for many products they sold themselves with their brand. And those have as much updates as any other company, well maybe one or two more.
I happen to have two devices bought directly from google. One is stuck on android 2.3 and another on 4.0, both full of security holes, not updated because "it would be too slow" when in reality i can't even install replicant et al because google never worked with the component providers to offer compatible binary blobs for the hardware.
Yeah, android itself is opensource (mostly because it is built on top of GPLed linux code so they do not have an option) but 99% of what makes your phone run is a proprietary binary-only code provided by the likes of Qualcomm etc. And why phone manufacturers, google included, use the options with closed source binary blobs? To save $5 or so from the BOM cost in production.
I'd also argue that even if someone uses Play Store services, but doesn't pay a penny, they're still a "customer" in a looser sense of the word. They're engaging in the market-place, likely using free apps subsidized by advertising. Even if you want to argue that they're the product instead of the client (and I'd be inclined to agree), they're still revenue-generating users.