Intake of information is Se/Ne/Si/Ni. Processing of information is Ti/Fi/Te/Fe. I'd say you need both steps to "rapidly figure out scenarios". Ne is no more "rapid" than Si/Se/Ni, it's just different. Si might be instantly like "I bet the cheese is burning, that happened to me last week", Se might be like "that smoke smells like cheese burning", Ni might be like "I think there's a connection between the smoke and excessive cheese I put on the peppers" (ok, I have no idea for Ni) and Ne might be like "smoke could come from the peppers! the oil! old bread crumbs! random socks in the oven! cheese! let's go with cheese" ....or you know, something along those line. The information you take in has a different flavour, a different focus, but it's not like Ne is better or worse at suddenly seeing solutions. That there is called intelligence, not Ne. Believe it or not, those two things aren't interchangeable.
As far as problem solving, that's the stereotypical domain of Ti. Ne-Ti tends to head more towards abstract problems and Se-Ti tends to head more towards real-life problems, but Ti is the main player there. It's not even that Ti is necessarily better than other types at problem solving (MBTI measures preference, not ability), but more that it's drawn towards problem solving and might continue to work away at the problem after other types have gotten bored.
And to restate the obvious, type is frequently not the best explanation for things like "being good at X". It may be part of the answer, it may be irrelevant, it may go counter to what you would predict from type.