The hardware that is capable of doing that (and more) is high end now. With how quickly this technology is advancing, it won't be low-end by the end of 2016, but neither would it be high-end. Just a medium level technology. You have to realize that phones are running at resolutions 4-8x 720p, and while gaming might not be too heavy, there are other GPU heavy tasks these phones will be accomplishing. 

http://kyokojap.myweb.hinet.net/gpu_gflops/

And here is an article on PowerVR advancements (for information on powerful hardware that isn't Tegra.) 

http://www.macrumors.com/2014/11/10/imagination-powervr-series7/

These are suppose to reach this year, so they should be high-end this year and mid-ranged next year. 

But can we rely on Nintendo to opt for these modern parts instead of the mature (read: withered) graphics technology they tend to favour? And if it's coming late 2016, when would they be choosing parts, this year?

In the past, technology in the mobile arena wasn't advancing very quickly, so Nintendo could have comprable performance for older, cheaper parts. For example, in the original NDS its ARM 9 processor was released in 2000, but the ARM 9 which released in 2004 wasn't much better, although I'm guessing more expensive. The same thing for the 3DS. What we see with Nintendo is that while they don't choose the newest parts they will choose parts that are comparable to certain newer releases (being newer =/= better.) So maybe the next handheld might not have a GT7600, but it might instead have a GX6850 (three years old by the time of release)  which is superior to the GT7600 (assuming they went the POWERVR route.) Also remember older parts might not always be cheaper. There must be a manufacturer around willing to produce them in bulk. Back when the DS released and even when the 3DS released Mobile hardware wasn't changing that rapidly. So older, outdated technology would linger and be accesible more easily and costs for these parts would remain low. Now, it would be very hard for Nintendo to find a manufactuer who will put a four year old GPU into their handheld. When the DS was around, it was no problem to get a 4 year old CPU, as the hardware was still frequently used. 

Also Nintendo will make decisions based on manufacturering costs at the time of release, not the time they put the GPU in. 

A very thorough explanantion, thanks.

I just hope Nintendo sees and seizes the opportunity to take advantage of the rapid progression of mobile tech.

I was getting the resolution from http://en.wikipedia.org/wiki/Nintendo_3DS, which has the resolution at 

800×240 pixels (400×240 pixels per eye, WQVGA)

so 480p would only be double. It is wiki though, so could be wrong...

That would certinly be the smart thing to do, make its construction as standardized as possible to keep costs down. But sadly, Nintendo don't always do the smart thing. Look at Wii U; it's way overpriced for its power level. I don't feel I can trust modern Nintendo to be commonsensical and achieve a power-to-cost ratio as good as nvidia.

It would be quadruple quality. 3d is still 400 x 240 on 3ds.

Si why would it be quadruple quality? isn't native 480p 800X480? 

Because 3ds resolution is 400 x 240. 800 x 480 is quadruple.