You call it on the cheap, yet the 1070 by itself is more expensive than the Xbox 1 S. You'd still need the CPU, MB, RAM, HDD or SSD, case and operating system on top of the 1070 to be able to do anything at all.
I'm pretty sure the Nvidia Shield will not natively play games in 4k.
However, it would be good for Nintendo do at least think about being able to display games in 4k, even if they have the tech level of the One S in the system. Being left behind even that is not a good idea at this point.