The single-button approach is valid, IMO - for the right audience. I hated it myself... and then I had to help my parents and grandparents learn the ropes with mobile devices. Turned out that iOS made them more comfortable for one simple reason: no matter where they ended up, if they felt like they were lost or overwhelmed, there was always that physical button, looking the same, and in the same exact place, that they knew would backtrack them back to "the beginning" - i.e. to a known state from which they could try again to do whatever they wanted.
So, in some ways, it is genius, and I really hated it when Apple killed it off. The problem wasn't the concept itself - it was trying to sell it as UX for everyone. I think that's one of the big problems with UX today - the things that are done under the guise of "simplification" aren't actually simple.
The problems posed by multiple mouse buttons are very similar to the "hidden swipe gestures" people are complaining about elsewhere in the comments for this article. There's nothing inherently wrong with either - any more than there is with e.g., English being a language with thousands of "hidden" words that people have to learn and remember instead of limiting you to only the words visible in an autotext menu - but you have to think about how people learn them, how consistently they're available, how to accommodate people not knowing them or learning them at different rates, etc.
HN commenters tend to be power users of desktop-style UI more than touch or mobile-style UI which can make it hard to see similarities between them (right click conventions really aren't much more consistent or obvious than swipe conventions)
I will disagree on that last bit, again, based on personal experience. Right-clicking to produce a context menu in Windows was easy to explain to my mom, and she very quickly started to use it everywhere to discover the available actions - and it worked. In mobile UIs, on the other hand, to this day, she is struggling to figure out where you're supposed to press-and-hold, where you're supposed to swipe etc. Quite often, she'll do press-and-hold to do something that worked in one app, and it doesn't work in another. Desktop apps are much more consistent in that regard.
So, in some ways, it is genius, and I really hated it when Apple killed it off. The problem wasn't the concept itself - it was trying to sell it as UX for everyone. I think that's one of the big problems with UX today - the things that are done under the guise of "simplification" aren't actually simple.