Yeah.
Naturally an Ne+Fi person will use Fi to help shape the connections that Ne makes... just like Ne+Ti will create connections using more literal/natural law (sort of like Wile E. Coyote style logic, it's all "sensible" according to the laws of nature).
I think ENTP can seem sort of insane -- mad scientist -- when Ti is off or extremely rigid, and so Ne is fettered and bound to it and thus distorted by it. Ne becomes enslaved to Ti's desires, rather than Ti "giving advice" to where Ne goes.
Likewise, depending on how strong and how "rational" the Fi is, the Ne can become completely muddled and enslaved into supporting the rigid Fi valueset.
The healthy ENFP's are wonderful, they explore everything and merely let Fi guide where they go, to inform their steps, rather than twisting Ne to justify Fi's rigid demands all while still retaining an extroverted energy flow. The extroverted energy flow coupled with Te skill also can result in someone who can be domineering and demanding and rigid/lopping off corners to force something to happen a certain way. Not a great combo.
Purely theoretical point: If you have a type where Ne is dominant and Ti is auxiliary, why is it the case that when this type becomes unhealthy Ne becomes subordinate to Ti? It seems to me that the scenario would make a lot more sense if it was the other way around: primary functions are dominant and the auxiliary are subordinated.
From a purely typological standpoint, I'd think if an unhealthy ENP was given full freedom to be true to his or her natural tendencies, he or she would be guided by the output of Ne and use the auxiliary introverted judgment to give him or herself an affirmative judgment in favor of the demands of the dominant Ne function. It does seem to be the case that you're onto something here, as you mentioned, the auxiliary Introverted Judging function seems rigid and demanding. However, I don't see any reason why it should be rigid and demanding in defense of its own output rather than the defense of the output of its master-function: Ne.
In other words, you're absolutely right that in this case the Ti and Fi can be terribly rigid or demanding (for example, the case of a mad scientist), but it demands support not for its own interests, but for those associated with Ne. Consider your example of a mad scientist who seems to fit the unhealthy ENTP image that you're describing. A person of this persona is almost never seen as a very dispassionate scholar who is concerned first and foremost with logical analysis, nor is he a systematic thinker. Hence, the attributes associated with somebody who is guided first and foremost by Ti are not descriptive of his habits of thought.
In other words, he is nothing like a logician or a mathematician who may be very rigid, yet dispassionate and logically consistent. The mad scientist often makes wild speculations that almost nobody can understand or justify. His motives are far from dispassionate. On that note it seems far more plausible to say that this person is inspired by motives associated with Intuition rather than Thinking, and he certainly incorporates an element of Feeling into his disquisitions. If he was primarily relying on Thinking, Feeling would have been greatly suppressed, but that certainly isn't the case here.
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However, I think you've gone wrong altogether by using the typological analysis to describe an unhealthy ENP. The way an unhealthy ENP would behave in daily scenarios would heavily depend on his or her circumstances. For instance, if he or she works for a corporation, regardless of how much he'd like to act like a mad scientist, he simply would not have a chance to.
Although if this person does have an opportunity to be true to his natural dispositions, the typological analysis provided above applies.