i mostly agree with you, especially that 'the challenge is to return to harmony with nature while still enjoying the benefits of science and technology'
vaclav's 10% goal is obviously not enough. we need to be able to capture more like 150% of current co₂ emissions, not 10%. his argument is very weak, though, so weak that he can't possibly be expecting to convince anyone who doesn't already agree with him; his argument is that the mass of co₂ you'd have to handle is 4 billion tonnes a year (because the total is 41.2 billion tonnes a year https://en.wikipedia.org/wiki/Greenhouse_gas_emissions#Data_... if we only count co₂), and that's an implausibly large amount of mass for a new global industry to handle, because it's comparable to the amount of mass handled by the oil industry (82.8 million bbl/day according to https://en.wikipedia.org/wiki/List_of_countries_by_oil_produ..., which does indeed work out to about 4 or 5 billion tonnes a year)
this is a very weak argument because there are several industries that handle more mass than that. https://en.wikipedia.org/wiki/Concrete#Construction_with_con... says about 7.5 billion cubic meters of concrete were being produced per year in 02006, which works out to about 20 billion tonnes; more recently, https://en.wikipedia.org/wiki/Sand#Resources_and_environment... says 9.55 billion tonnes of sand were consumed in 02007, and in 020222, 50 billion tonnes of sand and gravel, mostly for concrete. water withdrawals from freshwater sources, mostly for irrigation, are about 4 trillion tonnes per year: https://www.statista.com/statistics/1258433/water-withdrawal... of which 13% are municipal. (https://en.wikipedia.org/wiki/List_of_sovereign_states_by_fr... agreees that it's about 3.90 trillion tonnes per year.) we can roughly estimate that those 500 billion tonnes of municipal-use freshwater produce 500 billion tonnes of sewage; https://en.wikipedia.org/wiki/Sewage#Flowrates says the average is 35–90 liters of sewage per person per day, which works out to 100 to 250 billion tonnes per year, which is a dismaying discrepancy from statista's unsourced figure, but still close enough to establish that we're not talking about a mere four billion tonnes of sewage per year
so establishing a new industry that handles 60 billion tonnes a year of carbon dioxide (150% of current emissions) is a completely plausible thing to do, even at the current level of economic development. currently it's too big a job for any single country
smil also implicitly expresses some skepticism about the idea that you can keep the co₂ in the ground once you pump it there. that's just because he's completely unfamiliar with the field; gas in natural gas deposits has kept its co₂ (a useless diluent) underground for tens of millions of years, and some of those gas fields are being used today for co₂ storage, but also it turns out in the recent experiments with mineral carbon sequestration that olivine-rich rocks deep underground serpentinize extremely readily when you pump concentrated co₂ though them, after which they are known to be able to retain it for billions of years. those rocks are available everywhere on earth
now, keep in mind that these numbers are all at our current level of economic development. with ten or a hundred times as much energy, we'll be able to handle much larger volumes of material
which brings us to your argument, which is a much stronger one than smil's: getting those 60 billion tonnes a year out of the atmosphere will require much more energy than getting the same amount of sand out of ancient seabeds, water out of rivers, gravel out of quarries, or sewage out of people's butts. i can't find my calculations at the moment, but plausibly it would require about 10% of world marketed energy consumption, a couple of terawatts. there are various high-tech scrubbing materials like synthetic zeolites and triethanolamine, but soda-lime would work fine and is much cheaper; it just has to be heated to a higher temperature to regenerate it
i'm not sure why smil doesn't mention this, because it's a much better argument than his actual argument and he must have heard of it, but at least in the segment you pointed to, he doesn't. it's possible that he's too unqualified to understand why it's a better argument
so that's why i think a lot of economic growth is needed in order to put atmospheric carbon capture into action