In combination with drastic emission reduction cuts, limiting global warming below 1.5 °C or 2 °C requires atmospheric carbon dioxide removal (CDR) of up to 16 GtCO₂ yr^-1 by 2050. Among CDR solutions, ocean afforestation through macroalgae cultivation is considered promising due to high rates of productivity and environmental co-benefits. We modify a high-resolution ocean biogeochemical model to simulate the consumption of dissolved inorganic carbon and macronutrients by idealised macroalgal cultivation in Exclusive Economic Zones. Under imposed macroalgal production of 0.5 PgC yr^-1 with no nutrient feedbacks, physicochemical processes are found to limit the enhancement in the ocean carbon sink to 0.39 PgC yr^-1 (1.43 GtCO₂ yr^-1), corresponding to CDR efficiency of 79%. Only 0.22 PgC yr^-1 (56%) of this air-sea carbon flux occurs in the regions of macroalgae cultivation, posing potential issues for measurement, reporting, and verification. When additional macronutrient limitations and feedbacks are simulated, the realised macroalgal production rate drops to 0.37 PgC yr^-1 and the enhancement in the air-sea carbon flux to 0.21 PgC yr^-1 (0.79 GtCO yr^-1), or 58% of the macroalgal net production. This decrease in CDR efficiency is a consequence of a deepening in the optimum depth of macroalgal production and a reduction in phytoplankton production due to reduced nitrate and phosphate availability. At regional scales, the decrease of phytoplankton productivity can even cause a net reduction in the oceanic carbon sink. Although additional modelling efforts are required, Eastern boundary upwelling systems and regions of the Northeast Pacific and the Southern Ocean are revealed as potentially promising locations for efficient macroalgae-based CDR. Despite the CDR potential of ocean afforestation, our simulations indicate potential negative impacts on marine food webs with reductions in phytoplankton primary production of up to -40 gC m^-2 yr^-1 in the eastern tropical Pacific.