I don't think anyone says that unused ferts are a cause of algae, but rather the imbalance associated,
Well, many of the soil ferts only crowd sure like to suggest and some outright claim this. When pressed, they hedge, going with "the imbalance" malarkey...............yet never being specific about what the imbalance is, leaving the question very much unanswered.
There's no "imbalance" (what the frick does that even mean?). There's a limiting factor, maybe N, maybe P, maybe CO2........they do not know.
They do not test sediments or nutrients there, just the water column, the nutrients are in the sediment however, so test kits are useless for them in answering this question.
They only way to know is from the plants' health, but that can be influenced heavily from poor CO2 etc. Good health you can be fairly confident about(sort of serves as a control reference), but poor health could be many things. Only if you induce it on purpose specifically, can you figure those out and what they look like. But few, if any, bother to do it.
"I don't know, something's wrong" is about all they got. Instead many suggest they do know when they don't. Some make stuff up, some based it extremely liberally on something they read off the web.
If you dose both locations, then you cover any and all limitations and both methods are enhanced/not left to such unknowns and chance. You hedge your bets so both locations are well supplied of nutrients.
Then there's no "imbalance".
While it does not answer the specific question, it does cover all the bases for plants as far as nutrients. From there, you can look elsewhere.