I thought about this for a while today and in the end I can't say that I'd really care.
I was never a huge console gamer and I'm even less of a gamer in general these days (
"I wiiiiish I had time to play video games"), but everything Microsoft did with the Xbox One was absolutely disappointing for me. From the entertainment focus, to the price, to the lack of games or interesting projects that appeal to me. Don't get me started about 3rd party accessories or DLC policies.
The entertainment angle leaves me completely cold, too. I'm one of those few idiots who own an HTPC that ran Windows Media Center in the past and is running XMBC now. I've only seen the E3 presentation, but that didn't impress me at all. Live TV is completely dead to me (I don't even have a tuner in my apartment) and apps are everywhere else for me, without needing to pay for Xbox Live to access them (and XMBC supports AirPlay, too!). Heck, there's not even a remote for this thing. Are they expecting to conquer the living room with a game pad and voice commands that work only 90% of the time?
Lets assume Microsoft would ditch the Xbox brand, how would it affect the rest of the MS ecosystem? The Xbox app on Windows is a fancy wrapper for all the stuff you can see on Xbox.com. The Xbox Windows games aren't worth mentioning either. Xbox Windows Phone? 3 years going and a complete failure on many levels. Xbox Music+Video? I think most of us would agree that Zune was better in almost every way. Tags worked most of the time, it had a desktop and sync client that was beautiful and it supported video on the phone from the beginning.
What else is there to lose? The living room? I dare to say they don't even own a third of it. Consoles are such a small market. Even in their best quarter, Microsoft still couldn't beat Nokia's Windows Phone shipments of the last quarter or the one before. Now it's not fair to compare them, because of the price difference. But then again, isn't that the point? Microsoft is setting up a $499 box to compete with $99 throwaway boxes like the Roku or Apple TV. Hell, even Sony are better positioned with the Vita TV. The $99 disk-less Xbox 360 should've been a thing, but it's not.
Now this little rant is from my personal perspective and opinion and is obviously not in line with your experience, but really, I wouldn't shed a single tear.