This is all interesting analysis but you state that all functions can be active or passive (which is not quite the same as what I am saying) but then decline to substantiate the idea.
You want more? Oh. OK.
Active = problem-solving to reach a clear decision.
Passive = problem-solving to eliminate potential choices that might not be optimal or might even be harmful, or to provide more potential choices, such as when one's dominant has run out of options.
Usually, these modes work very differently. The active mode is more practical. The passive mode is more academic or theoretical.
Logic is by its nature rather passive. Sometimes it can reach a decision, but only very slowly. It would not be prudent to use logic as one's primary method of decision-making, at least, in this form. For this reason, people tend to think of those who base their life entirely on logic, as being rather unproductive. So there have to be However, if INTPs really lived that way, we'd not be able to decide what to wear before we leave the house. Likewise, if ENFJs relied entirely on their feelings to know what to do, they'd often just feel, but have no idea on what to actually do. So the functions that seem to rather indecisive, have to be decisive, to act as our primary method of decision-making. Likewise, the algorithmic functions that seem to only produce decisions on what to do, such as following the rules (Si), have to be able to provide useful information to another method of decision-making, to act in an auxiliary fashion. As these 2 ways of approaching the same algorithmic functions are usually described in very different ways, to explain what they are, might have to require different descriptions for each mode of operation, in an active decision-making mode in the dominant position, and as a passive aid to decision-making in the auxiliary position.
For instance, logic is useful to help us make a decision. But as a primary method of making split-second decisions such as in driving, it would be quite poor. We'd need something a bit more useful there. I eventually came to the realisation that when I make decisions in real life, most of them tend to focus on "whatever works for me". Most of my practical decisions are about "whatever works". But they usually involve solutions that wouldn't work for most people, and rely on my quirks.
I also use logic, in a more passive way, to help me figure things out. There, the decisions come later.
