The X1 released 2 months before they started constructing the Switch (2015); they were inclined to use that chip. The P1 was too expensive and wasn't released yet.

Nintendo already stated if they reach 10 million Switch units sold by the end of the year, they would either plan to make a reinforcement or cut the price. Besides, the Switch isn't obliged to require that architecture yet, unless most games can't even run at 720p30 bare minimum on handheld.

Oh, and before you say, "they could've waited", Nintendo were financially struggling and desperately needed a replacement for the Wii U, they couldn't continue creating games for that console and the 3DS was surely on it's way out after Sun and Moon. They wouldn't be relevant for a long time if they didn't reveal the Switch sooner than now, and that could indirectly butcher the success of the Switch.