Yeah, I recall the Xbox being super popular to pick up for the sole purpose of repurposing into a media center (the main OS being the Linux distro Xbox Media Center (xbmc), today known as Kodi)

It was as much a pragmatic choice as an inspired one; commodity pc hardware was obviously getting close to cheap enough. Others have suggested Microsoft lost money with this move, even if so it was probably still a pragmatic choice. Microsoft were entering a market that has been notoriously unfriendly to new entrants and spending more on hardware to ensure a successful launch of such an ambitious brand could be argued to make sense, with consoles able to recoup hardware loses in software revenues.

It was likely more about making it easy to port existing windows directx based games quickly and cheaply. Similarly, it granted a development stack that a great many developers would already be somewhat familiar with. All good things for a new entrant to a tough marketplace.

Presumably it also allowed them to get to market faster? Much less custom silicon?

"Revolutionary" is probably not the right term, at this point it was pretty much inevitable given the progress of PC hardware, but it was ahead of the curve by necessity.

Didn't they have to kill it only a couple of years in because it wasn't cost-effective? IIRC it was sold at a huge loss that they never managed to get back.

The original Xbox had some contractual problems that prevented it from being cost-reduced. I don't think MS cared if they broke even since they were in it for the long haul. Everybody knows Xbox 3.11 for Workgroups was the first good Xbox anyway.

Very different from the Windows Phone philosophy, then.

Not necessarily. PS2 dominated its generation; Xbox did OK, but only a company Microsoft's size could have sustained it (and even Microsoft superseded the console in four years, unusually short for that generation). Xbox 360, Microsoft's second try, was hugely successful, beating PS3 everywhere outside Japan. Had it only been as successful as Xbox was, though, Microsoft might not have tried again.

No Windows Phone iteration ever had more than a few percentage points of share. iOS and Android both clearly destroyed it in the market. Had WP seen a few years of sustained success it would still be around today, sort of like how BlackBerry the brand is still around, albeit for Android-based devices.

The Xbox 360 only beat the PS3 in English-speaking countries. By the end of the generation the PS3 had outsold it world-wide, if only barely.