Speaking as an American
(who, I must admit, has only started reading Piketty's book and has only a generalized knowledge of his argument), I can say that Mr. Worstall's take is completely beside the point. On this side of the pond, income for the masses has been stagnant since about 1974, while prices have continued to rise. Both income and wealth have risen for the top 10% and more so for the top 1%, to the extent that income for some CEOs has been clocked, in at least one instance, at 750x the income of the lowest paid worker in the same company (more commonly being a mere 250—300x). The welfare state here is not nearly so generous here as in the UK or Sweden (or France, for that matter). Medical bills are one the most common causes of bankruptcy. The current attempt to remedy this (which I call the Insurance Industry Protection Act) was a Republican idea now repudiated by said Republicans, because it was passed under a Democratic President. (Admittedly, it's a hot mess that would not have occurred had Mr. Obama lived up to his promise of a 'public option,' but that's an argument for another time.) While coverage is somewhat improved, we are now mandated to pay for it (which the Right and Mr. Worstall no doubt term a tax, and a largely regressive one at that). Of the 45 million uninsured, there are now only some 28 million... But enough of insurance and healthcare.
Even those working today can find it hard to make ends meet. WalMart workers are infamously often on EBT (née Foodstamps) and Medicaid. True, the poor are nowhere near as poor as the poor of past centuries, and that's good, but it's not really the question. (When I lived in Holland in the 70's, they said under the Dutch system you can't soar as high, but you can't fall as far. At this point in the US, you can soar with eagles but you can still be driven into the ground.)
There are two things, to me, that are especially germane: gross societal inequality, where 90% of the assets are in the hands of 10% of the people is a leading cause of economic catastrophe, as in the Great Depression. The other is societal and economic mobility, which except for a few, has all but ceased. This means that top percentiles stay rich, and in a land where by law money equals speech, they take control of the levers of power and warp the nation to their personal ends, which becomes a kind of economic feedback loop. One can see a future where 'wage slave' is not hyperbole.