The most fundamental problem with the entire argument is that it sets up a straw-man that reflects a fundamental lack of understanding of the basics of economic growth: that economic growth means resource depletion. While it is true that if you find a valuable resource and exploit it you are often contributing to economic growth, the same is true if you invent a new solar technology that allows people to use only sunlight to power their homes. In either case you have created stuff that people want and value and this, not resource depletion, is the source of all economic growth.
The same straw man is used to equate consumption with resource depletion. Again, we can all have rising consumption without resource depletion. In fact what most distinguishes wealthy societies is how much more leisure we consumer than do poorer societies.
As usual, population growth is thrown into the mix without recognizing that a key correlate of population growth is poverty. So how do you tell a poor farmer in India with no retirement, no social security and no insurance that he should not have multiple kids to help him out? You don't.
Which is why this argument bothers me so much, because I have dedicated my life to trying to improve the growth trajectories of developing countries precisely because I think it represents the solution not the problem. With higher incomes, societies have fewer children, value the natural world around them more, can afford to invest in cleaner technologies, and so on. It is only through growth that the world can overcome some of the most pressing worldwide challenges that confronts it.
This idea that growth has been bad conveniently ignores the vast improvement in infant mortality, life expectance, morbidity, etc. experienced in the 20th century. Instead statistics about subjective measures of 'satisfaction' are used never mind that ones perception of their lot in life has a lot to do with what they see in their community.
Which is why this idea that there is some grand mechanism that we control that drives growth is absurd. Growth comes from the desire of every human being on the planet to better their lot in life. Growth is inherent in who we are and what we strive for. How you actively control growth is unclear - a soviet style command and control economy? History has shown that to be an unsuccessful method of organizing on a national scale, one imagines how much worse it would be on a global scale.
Finally, the fatal flaw in the argument of the so called "steady staters" is that they profess to offer a better alternative. This suggests that people will be better off in their version of the world. Well if this were true people would value this new paradigm and therefore the new paradigm itself would create value and, oh dang...growth! Nooooo!
So talk about resource depletion all you want but don't conflate it with growth. The challenge of the 21st century is creating growth exactly from the invention of technologies that allow us to do more with less, not from finding more. Just because the 20th century was mostly about finding more and exploiting it does not mean this defines growth.