Where did the resources to put them into cryonics come from?
From... what they earned while alive (or in rare cases, from others who choose to spend earnings on them). Where does any resources for anything come?
Consider the few data points in recorded human history: Has the doubling time of economic growth remained fairly constant, or varied widely?
'Few'? Exponentials have been completely unambiguous for like 500 years and datapoints before then can be fit to an exponential.
Is it more complicated to assume that growth in in general exponential, with the amount of free resources determining the exponent, or to assume that the size of the economy is proportional to the product amount of the most-limiting resource at the time (Labor, arable land, electric power) and the efficiency of use of that resource at that time?
I've never heard any economist say global growth and the Industrial Revolution was just this 'proportional' thing you are talking about. (eg.the Solow growth model without the 'technology' factor fits observed growth even worse than with the technology factor.) And I'm not sure what you're saying even differs from an exponential - what is an exponential but proportional growth, repeated every year?
So no, no further discussion is necessary. The point about cryonics patients helping long-term economic growth follows from the most basic points of economic theory and observed economic history.
500 years is 'few', yes. Especially considering that population~labor has been growing roughly exponentially for most of it.
With the advent of industrial equipment, labor is no longer as often the limiting factor.
Imagine you accept the main idea of cryonics, that if we freeze brains future technology is likely to be able to extract the encoded information and revive the person digitally. [1] While this currently costs about $120K/person, if we did it routinely to everyone it could probably get down below $1000/person. Which is interesting: the current cost of averting a death is around $1700, but someone who doesn't die of malaria is still going to die of old age, so you can't really say their death was "averted". While someone who is revived after being frozen wouldn't live eternally, they might get to experience thousands of years of subjective life. In terms of life-years, getting cryonics to be really cheap and paying for people to get it sounds like it beats GiveWell's top charities.
Aside from not agreeing that cryonics is likely to work, however, I don't think the value is actually all that high. A future world which would revive large numbers of people we freeze today would be massively different from the current world economically, but would still have constraints. There would be some number of digital people that could run simultaneously on whatever people-emulating hardware they have. Preserving additional 21st century minds would give future people the option to run revived people instead of new people, but I don't think it affects the overall number emulated.
[1] I don't think this is likely.
I also posted this on my blog.