Very interesting post. I often took "product sense" to be magic, I did not really understand what was it that made iPhone soar in sales when it introduced very little over a Nokia S-series I had at the time and didn't even have a keyboard. Reasoning alone did not suffice: I could explain success of OS X (a UNIX that ran on commodity-ish hardware that "just worked" -- I did not have to rebuild my kernel to get a WiFi card to function!), the iPod (ease of iTunes/ITMS/using a large hard-disk instead of a 128mb
flash...), but not the iPhone.

When I (reluctantly) went to pick up an iPhone 3GS two years after the first iPhone's release, I began to "get it" -- it wasn't about a feature matrix, but the quality (including visual) of the features it did have and (most importantly) the way these features played together. Within minutes of having an iPhone I was able to use capabilities that my Nokia phone claimed to have, but that I have never found particularly useful/usable. Technically I could use cut-and-paste to share articles from the web browser on my phone via email, but I never did (but I began doing it daily on the iPhone!); technically, I could I could run apps on the Nokia but the only third party app I remember loading was Google Maps, etc...

iPhone was far from the first smart phone, but it "democratized" use of smart-phone as a smart-phone: while it was still a toy largely for the well-to-do, it was no longer a toy solely for a small fraction of well-to-do technical intelligentsia.

I could apply reasoning to retroactively conclude that "yes, iPhone is a great product"; however, it would take intuition to guess that right off the bat or much less formulate what features would be vital to a consumer smartphone. The popular image is that intuition is compartmentalized, innate, and unreachable to training, practice, or (especially!) learning. I suspect the reality is that talent does play a huge role (there's no way around it), but it is possible to deliberately cultivate at least some forms of intuition.

That said, what's even more amazing is when one develops a sense of gamechanger/show-stopper/distraction intuition about a topic that's not in their domain of expertise. There's an anecdote that when Steve Jobs visited Xerox Parc and met Alan Kay in the late 70s/early 80s he remarked that OO will be hugely important to future of programming. What I find amazing about this is:

1) Steve Jobs was not a software engineer, much less a PL wonk

2) In hind-sight the remark is obviously true

3) It wasn't a foregone conclusion in the 1980s, even among programmers. Smalltalk and CLOS were seen as crazy ideas in the 1980s, who knew that in 20 years large bulk (if not majority) of programming would be done in an IDE, in object oriented languages that run under virtual machines... Image based persistence was seen as one part of Smalltalk (and some Lisps) legacy that would never take off, but with user-accessible file system going away in iOS I am not so sure...

tl;dr Intuition about products in a specific industry can certainly be cultivated and learned (with hard work), but intuition about unknown (even if interrelated) product industries (or concepts) still feels "magical".