This is 2019, not 2013....Average PCs will be able to do 4k easily.
However I have a new conspiracy!
The DS (through all its regenerations) had a shelf life of 7 years before it was replaced by the 3DS which means in 2011 it will be 2018 before I see the next gen handheld. Nintendo home consoles have an average life of 5 years (Wii being the exception), and in 5 years it will be 2018. Nintendo have recently merged their handheld and home console departments.
AND with mobile devices soon to surpass the PS4 and XBO in power in 5 to 7 years time - and with mobile devices being able to already doc into your TV I hypothesise that Nintendo will only come out with a handheld system capable of both being an exceptional handheld gaming device rivaling the mobile market, BUT an adequate home console more than capable of rivaling the PS4 and XBO. The only thing is that I'm not sure of is the power, it'll be relatively cheap, but by today's standards it will be far more powerful than one could imagine having in a handheld device in 2013.
I'm hoping for a 2k system that can upscale to 4k, or that Nintendo can push the hardware to run in 4k but third parties would struggle to do due to the market for 4kTVs being increasingly popular by 2018. But more likely it'll only be a 1080p 60fps machine that everyone will laugh at for being under-powered. With everyone saying "Hello, and Welcome to 2013" even though it'll clearly use AMD GPUs invented in 2015/2016 miniaturised and modified to add extra oomf and use less power, of course it will use a modified multi-core espresso CPU
Why would Nintendo try compete with 5 year old systems?