The "advances" are relatively modest efficiency improvements, but they don't change fundamental realities like the laws of thermodynamics.
"Unburning CO2" will require enormous amounts of energy. You may shave off a few percent of losses here and there, but the amounts are so huge, it is absurd to think that you could do that and just continue business as usual.
For your example of cars it makes even less sense. You have no practical way of capturing the CO2 from cars short of taking it from the air. So you added another extremely energy intensive process.