The argument about government goods and services is that we can’t know their monetary value to consumers because they are not voluntarily purchased on the market. Of course, our use of them indicates that we value them, but it doesn’t indicate how much we value them. Therefore, it is a fallacy to add government expenditures used to provide their goods with consumer purchases of privately produced goods as if government expenditures had the same meaning as consumer purchases.
I’m not disagreeing with what you’re asserting Mises claimed. No index could ever be formed in comparing one set of goods to another because there is no common unit in which the goods can be added up that doesn’t itself change over time. Assessing whether or not standards of living have risen is economic history not economic theory. By nature, it’s not scientific. But who would deny that if you look at the set of consumer goods a typical family had in 1912 in America and compared it to the set of consumer goods a typical family has in 2012, that standards of living have risen in the past hundred years.
Your quote by Sowell illustrates why economists look at real wages and per capita income. If you look at real wages there is evidence of stagnation. The question is what are the causes? My contention would be that the 1970s and the 2000s were periods of dramatic booms and busts while the 1980s and 1990s were more normal periods of economic progress. The reason for this pattern has to do with the USA going off the international gold standard in 1971, re-establishing a dollar-reserve standard in the early 1980s, and having the dynamics of that international arrangement play themselves out in the 2000s in a way similar to the collapse of Bretton-Woods in the 1960s.