I'm sure there are low-hanging opportunities where this makes a good amount of sense. Places where there are olivine-rich mine tailings -- somehow uncontaminated by heavy metals -- adjacent to a tropical shoreline. In those instances, then yeah, I'm sure it makes good sense to just shove them over to the beach and let decomposition do its thing.
However, pitching this as THE solution to carbon sequestration is much more problematic. At gigaton scale, you're going to run out of mine tailings quite quickly. After that, you're talking about mining fresh olivine, from locations that are increasingly distant to tropical shorelines.
This would incur tremendous energy costs, and I'm skeptical that its balance would work in favour of olivine. How much does energy is required to mine a 1,000kg of olivine? How much energy is required to move it (say) 100km to the shore? If that net energy were applied to other forms of carbon capture, would it sequester more than 1,250kg of Co2? If so, then in that instance at least, olivine sequestration would be a bad idea.
Even if the energy balance works out favourably, I'm still not sure it's a good idea. Mining doesn't just have energy impacts, it has tremendous land impacts. 7 cubic miles per year of olivine is a very large amount of material. If you don't like the local impacts of mining gold and copper and coal and shale and sand and gravel, then this would have an environmental impact similar to all of those put together. Which is too much impact. It is probably preferable to pursue a less-efficient sequestration strategy than to engage in something with this kind of side-effects.
So I'm afraid that the way this is being presented will trigger a lot of skepticism / opposition. This is a shame, because in certain edge-cases I suspect it's quite a good idea. Even if this only addresses a small percentage of the total problem, every little bit helps. I'd hate to see the baby get tossed out with the bathwater.