In fact they do…or at least they argue and support the position that a free market would not only be able to match our current level, but in fact would lead to a higher standard of living than the one we currently experience.
Obviously you can’t prove that XYZ would certainly happen, or they wouldn’t be “theories” and there would be no “economics” (As Mises said: “If it were possible to calculate the future structure of the market, the future would not be uncertain.”)
…but you can offer arguments and support them. That’s what those works do…which is much more satisfying to a statist asking such a question because it’s the kind of information they’re actually requesting.