There are three aspects relating to its feasible application - as distinct from theoretical considerations.
1. Is the process feasible? The slow reaction rate seems to be a significant obstacle. Additionally, these minerals are rarely pure and may vary significantly in quality from source to source, leading to a QA/QC problem.
2. Can the process be scaled-up? Contrary to earlier comments, there is no wide availability of these minerals, not at the scale needed to make an impact. Moreover, the material-handling side of the issue is not well addressed. It isn't a simple question of drawing a distribution network on a diagram: it's working out the economics of the mass mining, transport, distribution and application of these materials. People are working on this, but I have not yet heard a compelling solution.
3. Are there undesirable side reactions? This is what farmers will worry about. It'll be good if these amendments increase soil fertility, but that has to be demonstrated. Do these amendments alter the physical structure of soils or reduce their capacity to retain water, especially after carbon is absorbed? Do they form concretions over time that would make soils less permeable? Does the exposure to plant exudates release contaminants in soil?
I was involve in a project at a Canadian diamond mine in which the host rock - Kimberlite - absorbed CO2. This caused a decrease in its alkaline pH and allowed small quantities of sulphides to oxidize and release contaminants. Clearly, this is the kind of undesirable outcome that must be avoided.
Lots more to say, but perhaps some EW experts will chime in.