And for the record, "because it's their device, not Google's" should be as good a reason as any.
It's not 2005 anymore, a phone has all the computing power that most people need. In fact, most laptops are just phone boards these days. It's completely reasonable to ask that your hardware not be artificially limited by the software it's running so they can sell you a separate device that does the rest of what you need.
In a perfect world, my phone is a supercomputer capable of doing everything I'll ever want in a fraction of a second. And the thing standing between my current phone and a perfect phone shouldn't be my insistence on having a separate giant desktop taking up more space than is necessary.
I'm not sure if this is a weird use case or not, but given the number of iPhone apps that I have both used and written that have special handling for TV mirroring to improve user experience... it can't be /that/ rare.