Yes, it is called eutrophication and is a huge pollution problem. The dead algae that drops to the ocean floor get eaten by bacteria and through that depletes the oxygen, resulting in hypoxic dead ocean. No fish and no plants, which in turn kills biodiversity both in and outside the water.
Even if the goal was to store CO2 and we didn't care about anything else, the method has additional problems. With nothing living in dead zones except for algae, the methane gas produced by decomposing dead algaes has a high risk of rising to the surface.
Even if the goal was to store CO2 and we didn't care about anything else, the method has additional problems. With nothing living in dead zones except for algae, the methane gas produced by decomposing dead algaes has a high risk of rising to the surface.