Emm, what? I'd say rampant photosynthesis by cyanobacteria is not a great way to tackle climate change. Yes, it will draw down CO2, but also produce O2. O2 is way more reactive and toxic than CO2, and generally not something you want to have too much off (unless you want to burn/explode something that is).
Maybe another 'great oxygenation event' is not what we should strife for...?
That is aside from other potential negative consequences of cyanobacterial blooms, which generally kill other life through toxins or by shading deeper water layers (and subsequent oxygen depletion when built up organic matter breaks down, leading to death bottom areas in the sea)