The types are generally sorted as NF, NT, SP, and SJ because of Keirsey and his theory. It makes perfect sense within his theory.
And everything sensing related is based on the real world, it's based on reality. Intuition seems mental in nature, based on the possibilities etc, which is a mental thing. Sensing functions work within what's tangible, intuitive functions work within what isn't reality (they look to the future or to the possibilities generally). And to clarify both perception styles come from what people perceive is reality.
My thoughts on the matter were stated above basically. Judgments are mainly an internal thing, and since intuition is also mainly based mentally, they go hand in hand. That's probably what Keirsey thought. And same goes with sensing and J/P.
Ne is external. Pe extrapolates the situation at hand based on the sensing and intuiting attitude, reaching outward rather than working within what one knows like Pi does. Ne has a mental base.
Si is internal and is outwardly based. It's based internally because of the nature of Pi, to reference the system of information within you. It's outwardly based (keyword BASE here) because it's root is reality (to the person).
NP, NJ, SP, and SJ would most definitely work. Hell, I even use these for myself along with NT, NF, SF, and ST and all of the other possible combinations to analyze a type. But since it's based in Keirsey's theory, it's the most widely known separation of types. Thus that's what we use generally.
Hopefully that made sense to you.