It's all about rates - in a properly cleaned and chlorinated pool, the CT (concentration-time) kill reductions for pathogens and algae are much, much higher than their respective reproduction rates. For algae, it's species dependent, but the doubling time for a colony will be 4-6 hours in day light conditions. However, the CT kill rates are measured as log-10 reductions and on time scales of minutes (or seconds), not hours. The CDC has general guidelines for the appropriate log-10 reductions for various pathogens but it does not specify it for algae because algae is considered nuisance, not a pathogen. So if one looks at the biological literature, algae kill rates are effective when the HOCl/OCl- (hypochlorous acid/hypochlorite) concentration is around 0.1ppm (but can be lower or higher depending on the algae species). For the TFP recommended FC/CYA ratio (7.5%), kill rates for normal blue-green algae are effective. Mustard algae and black algae require higher levels of FC but are not typically found in clean and clear pools unless they are allowed to proliferate. However, once an algae bloom is allowed to start (typically seen as cloudiness), the reproduction rates can overwhelm the kill rates and you'll eventually exhaust all the FC and develop green water.
An FC/CYA ratio of 7.5% is more than effective (overkill in some sense) when it comes to common pathogens except for some rare pathogen like cryptosporidium, giardia, etc.
