What possible effect could drawing a lake down have in terms of controlling an algae bloom that is caused by septic and fertilizer run off in the summer?

To my knowledge that isnt why they have done it at all. They do it for shore perimeter weed control and to allow homeowners to work on docks, walls, etc. The summer is over and with it the cottage and seasonal increase in septic flow drops sharply (assuming). Nutrient levels fall, cyanobacteria blooms end. I've not seen one myself after mid September.

Am I missing something here, or is everything I read including even the non angled run of the mill articles stating just every day ongoings totally off the mark now?

The homeowners dont like the weeds, so they draw it down. They aren't doing it cause of killer algae!

Fix your septics, or destagnate the lake. For crying out loud, EVERYTHING is #*&!.