Although that was the case for the PSP, the PSVita's support seems to be mostly due to Sony's strong 3rd party relationships in general. Note how Japan is transitioning from PS3/Vita ports to PS4//Vita ports in spite of all those being completely different machines.
Those systems all were treated as different systems too, released in vastly different launch windows, with the portable coming significantly later in both cases in order to approach the console with a more affordable price. If the NX is just the same as those, you're basically saying that Nintendo is bundling two dev kits that have little relation to each other for no reason at all.
Nintendo obviously won't make a system knowing that it'll bomb, but they should be making a system expecting limited relevant 3rd party support, and solving their lack of ability of covering two separate ecosystems was one of the stated goals of the NX.
Obviously, they've talked about that before and failed to address it. Iwata has been commenting on software droughts and promising to solve them since the GameCube, after all. So, I guess it's possible that it's all just empty words and they'll make the same mistakes again, resulting in two 'NX' that are actually separate systems released close to each other with similar but different libraries cannibalizing each other while wasting development resources, resulting in empty schedules. I wouldn't call that a sound business choice though, but it seems to be a possible path for Nintendo after all of their mistakes in recent years.
Still, exactly due to those mistakes and how much it finally cost them, it seems possible they might be trying something different this time. By the point that a portable Mario Kart starts basically resembling the console ones with some different features and tracks, why not just consolidate everything into a single game? To hope for double dippers at the risk of damaging the brand? You might as well ask for them to turn Mario Kart into an annual series if that's your only point. They now have DLC for something like that.
That effort would be better spent in other games that could attract their own audiences too and expand both consoles' library variety, making them more appealing in general.