AMD has tried the mobile market. There have been several generations of silicon with built-in graphics and, supposedly, low power. If you haven't noticed it's because the tablet makers, and generally everyone else, completely ignored the AMD parts. AMD Bulldozer architecture and most everything else they make has sucked when it comes to competing as low power options which is why they have failed in the mobile markets. Intel used to suck too here, but they are now serious about that and everyone knows they have the resources to compete in any market they get serious about. While it was once the case that Intel needed AMD to ward off anti-trust issues, they are fast becoming so irrelevant that I now doubt that's much of an issue...keeping in mind that these days the issue is probably more about the EU than the US.
Intel fabing for AMD is a fantasy, older processes Intel would probably not even be competitive on price and the current and future process technology is ridiculously proprietary where design and fabrication are so intimately entwined it's quite impossible. This is another reason why AMD crippled themselves permanently when they sold their Fabs and ceased cooperation with their one partner who had the tech and resources to help them: IBM. Back when, there were endless rumors/speculation that eventually Big Blue would buy AMD. Sadly, IBM moved away from hardware too, a decision I personally suspect they will, in the end, regret.