Both MS and Sony tried Nvidia in the past. I believe Nvidia didn't serve them well in terms of cost vs performance. Nvidia as a huge market leader can charge extra. AMD needing to cover for the market gap is willing to do more attractive offers for MS and Sony.
Since Nintendo aren't competing head to head in performance and Nvidia has Tegra for smaller devices, Nintendo isn't experiencing the risks and prohibitive HW costs that Sony and MS are trying to reduce
Since Nintendo aren't competing head to head in performance and Nvidia has Tegra for smaller devices, Nintendo isn't experiencing the risks and prohibitive HW costs that Sony and MS are trying to reduce