Basalt carbonation has gained traction as a key technology for avoiding the worst consequences of human-driven climate change. However, our understanding of this method’s promise is likely inflated by the specialized conditions used in many of the most well-known laboratory studies and demonstration projects. For technological, hydrogeologic, and energetic simplicity, many basalt CO2 storage projects will likely inject supercritical, not dissolved, CO2. Thus, fluids in these systems are likely to have low alkalinity and low pH, in contrast to many experimental and demonstration studies. Here, we present a series of geochemical models that explore the dependence of carbon mineralization efficiency on alkalinity and therefore pH at conditions relevant to these proposed operations. We modelled the interaction of basalt with CO2 enriched, seawater-derived aquifer fluid with varying initial alkalinities at 60°C using a custom thermodynamic database incorporating updated thermodynamic data for relevant primary and secondary minerals. The results reinforce the notion that alkalinity is an important driver for carbonate precipitation, ultimately because carbonate minerals are up to an order of magnitude more soluble at pH <5 than they are at pH >6. Alkalinity increases of 5 to 10% proportionally increase carbonate precipitation in the models. Our results thus demonstrate that the elevated alkalinity found in many of the most well-known basalt carbonation studies yield disproportionately high rates of carbon mineralization, which, in turn, frames basalt carbonation as an extremely rapid and exceptionally effective CO2 storage method. Although supercritical CO2 injection operations such as those we explore here are likely to achieve high fractions of CO2 mineralization over their lifetimes, this will likely take considerably longer and potentially be ultimately less effective, due to sluggish rates of CO2 dissolution and alkalinity generation.