What is?
The primary resource needed to build a home is land. Do we have infinite availability of land in desirable areas to build on?
Take Phoenix, for example, once air conditioning became cheap and pervasive.
You can not make things dramatically cheaper by bringing only the cost of labor to zero. Your argument is circular!
We don't need "AI" to figure out that technological advances increase productivity. The problem with yout argument is assuming that increased productivity mean overall reduced costs. It does not.
Healthcare, housing, education all have gone up despite increased productivity. Then you have things that are already so automated that there is no way to make them cheaper unless sacrificing quality - food, clothing, etc.
Then we have all the types of consumer products that have prices completely decoupled from the cost of labor. No one in their right mind the "cost of labor" has any relation whatsoever with Apple charging $1000 for an iPhone and/or Motorola charging $180 for a Moto G.
The hypothesis of Baumol’s Cost Disease is that these industries are exactly where we should expect prices to rise because they’re still dependent on low-productivity-growth human labor.
If the premise is that AI won’t improve productivity in industries like healthcare, education, and housing construction, then why are we worried about “the dead economy”?
The mistake you are making is that you are assuming that a system where productivity per unit of labor is higher automatically translates into increased global output. It does not. This idea of a dead economy theory is precisely the concern we are heading to a world where machines can make practically everything on the cheap, but it won't matter because the moneyed class won't need to satisfy the demands of the general populace.
To illustrate the point: Facebook laid off thousands of developers at the same time that it was hiring AI researchers, paying them tens of millions of dollars as a signing bonus.
Online advertising is a competitive business, so that means more bang for the buck for Facebook’s advertisers. Now those advertisers have more money to invest in making more / better of whatever they make.
1) We are talking about reducing the cost of labor, not overall costs.
2) Your logic only applies in the micro, not on the macro. If the cost of producing one thing goes down while population keeps their purchasing power, then what you are saying would make sense. The whole point of the article is that accelerated automation can bring a scenario where the cost of producing "things" would go down, but the economically active population would shrink drastically.
You just solved economics?