Another good example could be: think about the cost spent every year for lawyers to write EULAs or liability waivers that nobody reads, or to file tax returns that comply with our super complicated tax code. If the underlying legal system was simpler and/or less friendly to these liability lawsuits, the same effect could be had without needing any of those legal/professional billable hours.
That's debatable, because no one tears down a house and rebuilds an identical one.
* Was the old house livable? If not, then you haven't really wasted anything.
* Is the new house up to more rigid environmental standards?
* Does the new house take up more (less) space?
* Is the new house wired/piped in a different way?
etc.
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.
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.
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.
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.
The government could pay people to dig ditches and fill them back in, and that would contribute to the GDP even though it was a complete waste of effort and a net negative considering the opportunity costs.