So, here's my take on it. Sure, the processing power is a non-issue. That's all done onboard on the phone and passed through the "puck" out the HDMI cable. The car's display would literally just be a display device/monitor. The problem there would be that it would be ONLY that. Like, it would be on the phone "channel" and not able to display any other car data or info. So you'd lose potentially a ton of functionality.
Secondly, yes.. it acts like a desktop, but at the crappy resolutions those screens have? Yeah, I don't want a desktop experience on that kind of display. I'm going to label this idea (at least, as it stands currently by MS's implementation) as "spandex". That is to say, just because you "can" doesn't mean you "should".
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For what it's worth, I've been a loyal WP fan for many years. Took delivery of my '16 Passat last night and my phone is almost useless with it. I am now using a friend's Nexus 5. Plugged it in to the car and boom... worked like a dream. It even read Skype messages aloud to me while I was driving! That's something I was praying for Cortana to be able to do with WP. I mean... C'mon. It's Microsoft's own products! Why couldn't that work even if I was just running an aux cable to my headunit (gave up on getting BT pairing to work w/Cortana in an easy way).
MS needs to seriously step up their game in the automotive space.