This analysis is mostly accurate, and I absolutely agree with the conclusions. There is one point where I disagree though:
“One path to getting the deficit to 3% from its current 10% of GDP is to cut spending. However, this path carries the seeds of its own failure. Government spending is a big part of GDP, so cutting spending shrinks the GDP. The more spending is cut, the more GDP shrinks, which makes the deficit ratio less favorable. Adding insult to injury, government revenues expand and shrink in proportion to GDP, so cutting spending actually leads to reduced revenues, which leads to higher deficits, which lead to more cutting, which results in an endless spiral into the dumpster.”
Reducing spending would be the only way to get out of this situation gracefully (without a catastrophy) whether for the US, Europe or for any other country. And it would work - at least technically. Now I put aside the fact that reducing spending is political suicide and for that reason not viable in a democracy. So technically, if the spending was reduced, would that solve the problem of debt? My answer is: yes, over the long run.
US Budget deficit is currently roughly 1.5 trillion, budget is 3.5 trillion. Budget deficit is roughly 10% of the GDP so the GDP must be roughly around 15 trillion. So what would it mean if we reduce the budget to 2.5 trillion (budget deficit = 0.5 trillion)? GDP goes down (immediately) by probably more than the reduction in Budget, so lets assume a reduction of 2 trillion of GDP. This means GDP = 13 trillion, deficit is 0.5 trillion = 3.8%. Yes, we did not reach the goal of 3%, but we are a lot better off! (Even if you assume that each dollar not spent by the government reduces the GDP by 5 dollars, which I doubt, the percentage of budget deficit in GDP would be less than today, 5%)
As soon as we reduce the budget BELOW the government revenues, which must be around 2 trillion, we will have immediately no budget deficit. And that is exactly what we need to reduce debt.
Of course that would hurt a lot of people in the short run and no politician doing this would be elected again. But my point is: Technically it would work.
And now, as you already stated: Yes, the reduction of debt will happen anyway, the question is, if they wait until the US government debt explodes or if they try to reduce the debt gracefully.