The net reaction goes like this: CaSiO3 + CO2 -> CaCO3 + SiO2. Note that the products, silicon dioxide and calcium carbonate, are thermodynamically stable solids.

Crucially, the activation energy for the weathering of silicates to carbonates is low in the presence of water and carbon dioxide. Low enough that it happens spontaneously in nature on exposed rock surfaces. That means that the energy inputs required to reduce atmospheric CO2 via silicate weathering are much lower than a "combustion in reverse" process to turn gaseous CO2 into synthetic coal and bury it.

The other crucial issue is that the kinetics of silicate weathering are tremendously hindered in nature. A freshly fractured basalt surface weathers rapidly for a year or two and then develops a cation-depleted micron scale "rind" that drastically slows the weathering reactions with the rest of the bulk rock.

One way to accelerate the kinetics of silicate weathering is to use more concentrated materials, like the Iceland injection process: nearly pure CO2 plus water will react much faster than natural surface waters exposed to hundreds-of-ppm CO2 in the atmosphere. That works ok if you have a rich stream of CO2 like directly from a power plant's stacks. It won't work for dealing with CO2 already emitted to the atmosphere unless you add a complicated and energetically expensive pre-concentration stage to turn 400 ppm of atmospheric CO2 into a 950,000 ppm CO2 stream you can inject.

The other way to improve the kinetics of silicate weathering is to generate a lot more surface area: crush bulk stone into particles 100 microns or finer. Then there's a lot of fast-reacting extra surface area that can react with CO2 at ambient concentrations. And even the slow weathering to the center of the particle will take maybe a century rather than multiple millennia. (If a century sounds unacceptably slow, I would venture that you have not fully internalized the vast timescales that unaided nature would take to restore the pre-industrial CO2 equilibrium.)

Putting crushed stone particles in near-shore ocean environments may further accelerate weathering by ensuring that natural wave action keeps abrading the rind from particles. Crushed stone rich in magnesium and calcium silicates can also be applied to acid sulfate soils in tropical agriculture. Raising the pH of acid soils increases agricultural productivity by preventing low-pH aluminum toxicity to plants and, unlike sweetening soil with limestone, it sequesters some carbon at the same time. The crushed stone accelerated weathering approach can offset all sorts of CO2 emissions: point or distributed sources, local or distant sources, present or past sources. Finally, it restores the historical pH balance of the oceans as well as getting rid of excess radiative forcing from CO2.

The amounts of stone required to offset historical emissions are vast, but any solution will be vast because the scale of the problem itself is vast. In terms of scalability, simplicity, energetics, and flexibility, I think that accelerated silicate weathering is the best shot at long term restoration of oceanic and atmospheric CO2 concentrations to the pre-industrial baseline.