> (extracting oil -> refining fuel -> burning fuel -> sequestering carbon -> storing said carbon underground), the whole cycle probably provides negative energy

Very straightforwardly true. But if you add some steps: having an industrial revolution -> developing technology -> manufacturing solar panels or other renewables on a massive scale -> collecting energy for the carbon sequestration - you could imagine the human race coming out ahead.

Renewables can replace fossil fuels as an energy source. To undo a century plus of burning fossil fuels, you'll need a revolutionary energy source that outputs an order of magnitude more power. Maybe fusion, or maybe something that we cannot yet fathom. You can imagine this all coming to a happy ending, but at this point it's all up in the air. Both the CO2 and whether it'll ever come down again.