You can make hydrocarbons from c02 and water. Make digging up carbon illegal, so that only legal way to get your jet fuel is to buy it from a machine that makes it from the air (e.g. carbon-neutral fuels).
Under high temperature and pressure conditions, with expensive catalysts (I’ve had a grant to work on one of these processes a couple of years ago). It is completely uneconomical unless most government tax emissions very heavily one way or another.
Besides, this does not solve the capture bit, which is also a significant challenge, in similar ways (we have ideas about technologies, thermodynamics do not work in our favour, it would still require radical policies for it to work).
Nobody is going to wave their magic wand and make fossil fuels illegal anytime soon. It is a common techno-euphoria trap: technology is the easy bit, and we’re not there yet on that front. Policy is the struggle after that, and it is much more difficult.
A Dyson sphère around the sun would make life on Earth rather miserable.
> Successful governments should be responsible for running sequestrators on tax funding.
“Sequestrators” don’t exist. There is some noise every now and then about a fancy new technology, and it gets accepted in pop science media as something that works, but we don’t really have anything practical. Besides, this would be a terrible idea, because it means we lower the cost of operations for the industry, generating profits for their private owners, whilst straining public budgets already stretched thin. This would need a radical change of how most governments operate.