If we could store energy cheaper than we could use it we'd have a perpetual motion machine, I think? Fairly sure this would be physically impossible. Where this might be wrong is if we found a process to use another energy source (the sun, something that uses the sun, etc) to do it for us, but we haven't go anything that works in that vein either. Trees are actually one of the better options, but to reverse climate change you'd need to reforest the earth AND sequester all the oil we burned.
Burning carbon is effectively debt. If we stopped burning carbon right this second, billions would die, as our whole system depends upon it. But if we don't stop burning it, we increase our future problems.
This is unpleasant to reckon with so most don't. I don't think it makes the problem intractable, but it gets harder the more we delay.
We do need sequestration because simply eliminating all carbon sources wouldn't be enough, we also have to reduce current levels. Also there are some cases where fossil fuel might be the best solution (rocketry?) so we'd need to be able to deal with the waste.