The main issue with global warming is not CO2 or its removal from the air; it is the creation of new global policies and new way of thinking.
I recently watched a video that managed to freeze my bone marrow. It is about the simple physical and engineering facts when it comes to removal of CO2 from the air:
The video focuses on the technology and avoids mentioning the political dimension: currently we organize ourselves more or less efficiently at the level of the nation state (on the order of 100+ million people), but not at the level of the planet (10 billion people, soon). So organization will be the key to getting people to sacrifice 10-20% of their income for a 100+ year project. And based on the information presented in the video, that is the bare minimum.
Are there any examples from the past to show that this can be done? Well, most of the cathedrals in Europe were built as multi-generational projects. None of the original builders of the cathedrals expected to see them finished in their lifetime. Is there any other (basically useless, but more modern) kind of nationwide project that diverts huge percentages of a society's resources into building pyramids? Sure there is: https://en.wikipedia.org/wiki/List_of_countries_by_military_expenditures.
The main political problem with climate engineering is how to sell a project to people alive today when they cannot even be sure that their gran-gran-gran-grandchildren will benefit from controlling the effects of global warming. And how do you convince people to do something that is essentially useless to them? Well, propaganda, fear and ideology have their place in modern society. At the moment, the effects of climate change are already causing fear, but the petty political structures around the globe are currently channeling society's fears into the competitive game between nation states.
This is a problem that also requires an engineering solution; and increased militarization is not the right answer (for very obvious reasons).
I also see a lot of ideas on the net suggesting nuclear power as a solution to the problem of decarbonisation. I would ask these (otherwise obviously intelligent) people to imagine our world as it is now, where almost every nation state has access to nuclear technology and is using it to produce electrical energy for decarbonisation. Then imagine that for the next 50 or 100 years there are no revolutions, no nuclear accidents, no hurricanes that knock out power lines, no tsunamis, no asteroid impacts, and no people willing to sabotage nuclear power plants or subvert the technology to make bombs. And that all the nuclear waste (which will pile up) will be safely stored for the next 500 to 1000 years. Anyone who believes this has also bought into the idea of buying several hundred Brooklyn bridges. Every year. For the next couple of hundred years.
Bottom line: without radical changes in the way humanity organizes itself and manages this planet, we really are doomed to a much poorer and less secure existence, and no strictly technical approach to the problem can solve it. As always, the poor will pay a higher price than the rich. Some people would like to argue this, of course: "But is there a price to pay?" That debate should be over after this video, just as the debate about the shape of the Earth is over. So, spoiler alert: our home planet is not flat. And the frogs are starting to boil, along with all our water and all our air