That particular problem is indeed 1) very straightforward and 2) unsolvable. It's a major driver of the chaos. But that's just it - the situation is chaotic. There are many sideshows and complexities, and the upshot is that nobody really has any idea how it's going to play out. As shown by the elaborate diagram linked at the top of the page.
That problem is a sufficient condition for the chaos, and what has caused it. Without that problem, there could be consensus or not, and there could be other things to discuss, true. But that problem is enough to understand the current chaos.
You know what's funny? That even if the UK parliament never agrees and there is a no-deal Brexit, that problem doesn't disappear. In the event of a no-deal Brexit, the UK will be in violation of an international treaty (the Good Friday agreement), and the EU (and even the US) will ask them to honor the treaty. Fun times, indeed.
I wouldn't make any bets about what the US would do, sadly. I get the sense that the DUP and most people pushing for no deal actively want to tear up the Good Friday agreement (and blame the EU, even if that makes no sense).
I think this issue leads people to overestimate how much support the EU is giving to Ireland. How much they will support Ireland is still to be seen, but for now it seems to be more like "wait, agreeing to do what you already agreed to do is supposed to be the easy part; how can we negotiate with these people?"
IMO, the updated flowchart is way too optimistic. I don't see any reason to suspect parliament won't keep doing what it has been doing, either nothing in particular and crashing out or, more likely IMO, finding a consensus around an impossible plan, crashing out, and blaming the EU for not accepting it. If they were actually going to do anything different the time for that seems to have come and gone a long time ago. "Revoke article 50 if we can't come up with a plan" went down to a huge defeat Thursday as it has previously.
Edit: Looks like I should have checked the news first, sounds like there may actually be a general election. Edit2: Maybe not as clear as the headlines suggest.
It's not unsolvable, there are detailed proposals for how to solve it and after announcing loudly they would never work, the EU recently changed its mind and announced they'd already started preparations for it.
The only reason the Irish border is being described as "unsolvable" is because that suits the agenda of people who want the referendum to be ignored (as in Europe they always are).
