Well I know I remember at least a couple INFJs saying something similar- that figuring out 'what' right away isn't important, but knowing 'why' is. The 'what' almost takes care of itself once the 'why' is in place. How much that applies to ENFJ/ESFJ though, I don't know. (I'd guess it's the same.)
eta: More specifically, it comes up a lot that an INFJ will say they don't see the importance of focusing on identifying the immediate feeling in the throes of being upset because generally that feeling changes with new information. We want to make sure we've got the story straight (the 'why') before we bother figuring out 'what' we are feeling.
I keep going back and forth about whether to say something about my own experiences as another INFJ in relation to this. I may have kind of a weird twist on what you're describing here (I think ... um, maybe?). And I strongly suspect that what I'm describing below isn't simply Fe, but Ni-dom plus Fe. Actually I could see all of the top 4 INFJ functions interacting in this in different ways at different points in how this works for me.
So first of all, I personally find it useful to distinguish between feeling and emotion. The distinction I make is: feeling is a visceral response to something real in my environment (not necessarily physically concrete, but really happening), while emotion responds to something other than what is in the immediate environment (past issues, triggers etc). So for me, feeling is information that I can use to guide my action in my environment and interactions, while emotion isn't useful for that.
So feeling and emotion are very different things for me, but - here's the thing - they seem to use the same chemical/physical pathways in my body.
I've noticed a pattern in myself. I tend to incorrectly assume by default that negative feeling in me is emotion. What this looks like in practice is that
if I don't immediately understand the why of a feeling, I start explaining it to myself as probably about some past issue I've had or some current internal struggle I'm having - basically I find some plausible thing it could be about as an emotion, and talk myself out of it being valid information about my current situation/environment.
And then as things unfold over time, and whatever I was perceiving through feeling shows up visibly as externally real, I learn from newly visible (to me if not generally) external information that I was experiencing a real response to my environment rather than some inner issue I need to work out. (I'm not saying I don't have inner issues I need to work out, just that they don't show up this particular way). And the thing that gets me is, I have seen this dynamic over and over and yet I still have the default in myself to assume that when I feel something that isn't immediately visible in other ways, it must be emotion rather than feeling-perception of something real going on.
In all of this, I often to try to talk things out with someone else, but there's still something blurry for me about that process. It does seem to have something to do with getting externally-sourced information I don't have.
Trying to talk it through used to be almost completely about me trying to get some sort of reality-check about whether what I was feeling was real or not and if so how. The problem with that is that when something isn't visible and others around me have a stake in it remaining not visible, my reality-check efforts just reinforced my default and in the end failed and didn't map to the actual reality that eventually showed itself.
So I try not to do the dialogue-based reality-check thing as much anymore. Instead, I try to sit with the experience when I have a feeling. I try to encourage myself to shift into a default trust that this is more likely to be feeling than emotion given what I have observed over and over and over again in how this works for me. This effort to shift the default is pretty difficult for me still. I'm hoping it gets easier as I keep on it.
But in this process, I still do sometimes seek to process "what's going on" with someone else - trying to track down why I'm having the visceral experience I'm having. And pretty recently, something new is emerging beyond a simple dialogue based reality-check-in-words. It's actually a little intimidating to me. I'm beginning to get glimpses of an instinctive something in me that knows how to move to get the hidden (unknown to my consciousness) external information to surface so I can see it sooner than later. This is intimidating to me largely because a) I don't consciously know how I do this, I feel like it's opaque to my conscious mind what's going on when it's happening, to my conscious mind it feels like getting on a ride that gets me somewhere and this instinct in me is driving the vehicle and I only understand the method to its madness when the key information I need but didn't have actually emerges from the other person/people involved and b) it can be a messy and even painful experience that can include conflict with people I love.
I keep thinking there's got to be a way to be more deliberate in this process so I can get to the hidden external information in a less blurry/cleaner/more efficient way. But as of this point, I feel like my conscious self is pretty clueless about how the instinctive part of me does this. I can see the effects quite clearly, and it's really amazing what information emerges, and so far the information has been necessary at some very deep levels. But my conscious mind doesn't know (and can't even really track in retrospect) exactly how I do it.
I've been hesitant to try to describe this because I don't know if this has anything much to do with what you're describing, Z Buck McFate and I also don't know if it has anything much to do with the OP in this thread. But what the hell, I'll post it, Hopefully there's something relevant/of use here.