The seed money approach is not a bad approach. This would allow small research groups that the US government has decided to starve for cash to continue their work for a few years, and it also creates a bit more of a incentive, i.e, successive funding rounds. The approach does look more like a VC route than a federal agency approach, which has some benefits. The stories about how it takes six months and half a dozen reviews at a government agency to purchase some inexpensive lab equipment that was needed yesterday are not entirely apocryphal.

This approach seems interesting: > "Heirloom, a company working on capturing CO2 directly from the air, recently made headlines after raising $53 million in venture capital. For the XPRIZE, Heirloom teamed up with a company called Carbfix, which specializes in turning CO2 into stone. Carbfix is already demonstrating its technology at a working carbon removal facility in Iceland."

Note also that there's a real tie-in with SpaceX here, which runs rockets on a variety of fuels, i.e. RP1 which is essentially highly refined jet fuel, and methane, CH4. Mastering carbon capture and conversion technology, i.e. running processes like CO2(atm) + H20 -> C + H -> CH4, long chain hydrocarbons (RP1), would be critical to synthesizing fuel on Mars for example, which has an atmosphere of CO2 and apparently, water ice in the subsurface. This could also make SpaceX independent of fossil fuels: imagine a giga-scale carbon capture and methane synthesis factory in Texas providing all the fuel Starship needs.

Also, in a fossil-fuel free world, international air travel would require jet fuel, and that's possible with DAC and water-hydrogen, via a modified Fischer-Tropsch process, first used with coal gas / steam as inputs.