Yeah, I recently I've been scrapping this whole system model thing. It seems like only a weird detail. Not even part of a puzzle. More like the painting on a puzzle piece.
The system/model thing isn't so bad. It just needs refinement. Si has a model, whether Ti (logical) or Fi (impressionistic). Orobas calls it an "inner landscape".
Ni doesn't really have a landscape. Instead, it has this abstract map (Ni) that tells you where you are in the world (Se, Te, Fe).
That abstract map is fairly constant, but it can seem to radically change. Think of it like a huge gemstone. Ni can only tell others about one facet at a time. Each facet is superficially very different from the others, but they're all part of the same whole. When Ni seems to radically change one's mind, it isn't so revolutionary as it appears: the gemstone is rotated a few degrees, and the light reflects off the facets in a superficially different way. The changing the angle of refraction alone can change the light from blue to yellow, and so on. But the light itself stays the same, the gemstone stays the same. They just look different to everyone else.
Moreover, you're definitely correct that Si is not "tradition". It inclines toward tradition, but really it just has a very concrete model of the world. The world changes, and the model gets updated, more or less, but mostly it stays the same. Ni is just as static. That gemstone doesn't change. It stays the same.
Another analogy might be the law of gravity (for Ni). It's just F = -G*M_1*M_2/R^2. (Forget Einstein for a moment; contrary to popular opinion gravity still works mostly like Newton said, and Einstein's refinements are only important for the edge case like black holes, neutron stars, and massless particles like light.) That simple 1/R^2 law describes every bit of orbital mechanics you might ever observe (again, barring the extreme cases). But for every case except 2 bodies, the equations cannot be solved: they can be analyzed, or even have perturbation theory applied, but there is no exact analytical equation that describes how 3 or more bodies interact w/r to gravity. Instead we have to use numerical analysis (i.e., integrate the differential equations with a computer) to solve for any particular case. This is just like Ni. The inner rules stay the same, but the application of those rules can appear chaotic and inconsistent. For the 3-body problem, one trajectory can result in a fairly stable system of nearly circular orbits, while another slightly different trajectory results in all sorts of wild behavior, perhaps even flinging one of the 3 bodies off into infinity.
When Si sees this kind of result from Ni types, it looks like the "rules" have been changed. In Ni/Se terms, no rules have changed, but the specific circumstances (Se, Te, Fe) have changed, and the Ni-functional view predicts an entirely different result. Ni can seem stubborn to Si, because Si tries to change Ni's mind in terms of specific situations and data, without addressing the underlying functionality (the law of gravity). It seems stubborn because Si isn't talking about what Ni is thinking about. This also happens for other introverted functions, where the underlying terms in which one thinks are not (cannot) be directly expressed to others.
On the Si side, it isn't as if Si is somehow ignorant of science, ignorant of math or functionality. Rather, Si is focusing on concretely experienced data. Si retains that data very well. That Si data is its own map, and it can act like a "function", implying all sorts of things. But that Si-data is not easily communicated: one the one hand, there is too much data, and communicating it sounds like anecdotal evidence, and on the other, that underlying information is often obvious to others who use Si, so there is no need to communicate it. Ne (and Fe or Te) plays a role by drawing inferences from the data, finding patterns that are only obvious when one has a lot of sources of data.
The key is that Ni and Si "store" things differently. Ni remembers the functional interpretation. The verb. The adverb. (This is what you describe as a system. It's a system of behaviors, but not of objects, per se. The objects are interchangeable.) Si remembers the objects, where they were, when they were there. The noun. The adjective. It's a model, but it's a model that is kind of "static" for lack of a better word. The model doesn't handle the "time parameter" very well: time is a discrete series of events to Si, but a constantly flowing dynamic to Ni. Likewise, the Ni model doesn't handle objects and positions very well. It records interactions, and how they occur, but doesn't focus on what interacted.
The TL;DR version: Both Ni and Si use models: Ni is a functional model, Si is an object model.