It's not an invalid example. It shows that GDP has some weirdness. It's just not a scenario likely to be common enough to cause problems. But, it does demonstrate the leaky abstraction.

There are also scenarios that break GDP but not homo economicus logic. What happens when a woman starts working and paying for childcare? Do you subtract the childcare she is no longer directly providing as negative GDP? Do you just add on this new service as growth, even though the kids are not getting and more hours of "childcare?" This is a real problem with data pre 1960s and post 1980s. GDP can't measure those.

That's the economic equivalent of bulldozing a house and building a new one. There's a surplus, economic or otherwise but there is an unmeasured destruction too, parenting hours are reduced. We only count paid work so when one increases at the expense of another, the GDP abstraction leaks.

What happens if important new products and services are free, like Wikipedia, Khan Academy, etc? What happens when you can buy a £500 android phone for £200? Do you do an inflation adjustment that counts the value of all £200 iphones produced @ £500?

The real world mixes these up in ways that GDP can't really handle.

If one looks at this more broadly, the examples you bring up have to do with the fact that not everything can be reduced to monetary or market exchange (a distressing thought to some libertarians). This is more of the underlying problem than GDP itself which is "just" an accounting equation... Which is hard to use when there is nothing to account.

The question for society is , does this even really matter? We never used to subject ourselves to economics and markets as the totalizing sphere of human achievement, it was one of several areas of social organization alongside community, politics, family, religion, etc. We only start caring about this stuff when we want to compute dubious universal ultility functions and the like.

This is a little unfair to (intelligent) libertarians. A similar argument could be made for socialists or welfarists. They all rely on "economics" in the sense that they are quantifying and describing the dynamics of economic activity. Thoughtful libertarians know that these measures and models are representations of reality, not reality.

In fact, a fairly important figure in "neoliberal" thought is Hayek. Hayek (and Hayekians) argue that not only is the economy difficult to quantify and describe formally, it is impossible. In his frameworks price and choice are conveyors for knowledge.

I would even say that the most serious hubris in this vein has been the Stalinist and Maoist "5 year plan" which aimed to quantify economies in accounting terms.

I agree with some of your points: it was a little unfair, and Stalin and Mao certainly had great hubris. I tend to view libertarianism as the next desired grand social experiment: the Marxism of the Right. This leaks out via dry attempts at humor. Perhaps it won't be a disaster; I also admit I should be more respectful in a debating forum.

As for Hayek, I don't think he is unique in the view that price is about knowledge. While Hayek was the more readable and reasonable one between him and Von Mises, I'm aware the Austrians don't really believe one can scientifically study the economy, but I also think there is plenty of evidence that has refuted this: we can quantify and describe a large subset of the economy with predictive power.