I'm not convinced by carbon storage, though I don't know enough about it to be sure. It is my understanding that it is either energy-hungry (so useless because we don't and likely won't have enough carbon-neutral energy surplus) or pretty slow (also useless). And completely unproven at large or even moderate scales, too.
"Carbon storage" would normally refer to physically sequestering purified carbon dioxide or other carbon bearing compounds. I agree that storage of that type is not practical.
Enhanced silicate weathering is IMO the process with the best prospects for large scale atmospheric carbon dioxide removal. It is relatively slow but the thermodynamics are favorable and the kinetics are still orders of magnitude faster than waiting for unaided nature to restore the pre-industrial equilibrium. Enhanced weathering CDR just accelerates the kinetics of the natural chemical reaction that turns alkaline silicate rocks and CO2 into silica and alkaline carbonates. Doing it on a scale large enough to make a difference would be a gargantuan undertaking, of course, because the scale of the problem is also gargantuan.
Honestly, I am extremely pessimistic about mankind's ability to work on such a scale. Too many people seem to assume global warming is still a far-off problem, and that for some reason humanity is destined to "progress" forever, even though we know of many civilizations that have collapsed before ours.
I'd just like more people to grasp the dire reality of the situation, and stop assuming that somehow technology and/or progress will save us no matter what.