Why on Earth would they do that? It makes the whole thing more expensive, more complex and it limits their flexibility in different markets.
I'm betting on NX being a family of systems based around a common architecture, with a shared dev environment and software ecosystem, cross-platform accounts etc. - think iPhone/iPad/iOS or the Android setup. The device being referred to as "NX" right now will be the first form factor released, likely a handheld of some type, and it will hit some time toward the end of 2016. A more powerful home form factor will hit in 2017, replacing Wii U. From then on, Nintendo will be releasing software that runs on both, scaling appropriately, with the occasional title perhaps built for one form or another. As tech improves and component prices drop, they can release more powerful incremental upgrades (again, think the iPhone/Android phone model here) which maintain full backward-compatibility, even if forward-compatibility remains limited.
It lets them target different markets with different hardware - Japan may favour the handheld NX more than home NX, the US may be the reverse - while not having to support two different lines of software development. It also lets them release more regular hardware revisions and upgrades and breaks them out of the current console model.