You are beating a dead horse.
Algae actually has very little biomass relative to plants per unit area.
So you can doble that biomass in a short time frame, but the expect is still next to nothing relative to a plant, say duckweed which can double every few days, Azolla can also. But as the plants and algae grow at exponential rates, they become quickly limited by other factors and by space, self shading, low O2 levels due to respiration during the dark cycles etc etc.
Theory is one thing, reality is quite another.
then there's management of the ATS and export vs grabbing a handful of weeds and then selling them here on TPT.
I sold 250$ worth of plants this week.
When you sell 1/10th of this, 25$ for your algae, come talk to me.
In lakes, most of the biomass is algae because there's often not much plant biomass. You can design all you want, but the algae require more flow and mixing, and more light to even come remotely close, and those 2 things in artificial culture requires more energy. You have to manage this puppy also.
Aquatic plants for wastewater treatment. See Reddy and Smith, 1984,
ATS' are better at removing and maintaining very low ppb's ranges.
At higher nutrients, plants are better. Think about it like this : Elephants and mice are both herbivores that like grasses. Which can handle a low grass biomass area over time? Mice. An elephant can eat a lot more though when there's an ample food supply.
That's one somewhat imperfect analogy, but you get the point.
For planted tanks, we add NO3, we are not concerned about maintaining ultra low NO3 levels. Unless you raise cold water trout etc, no real reason to go this route. Non CO2 planted tanks tend to have N limiting conditions.
For reefs, where there is little input and export, they are quite useful.
Still, I'd say the Zooxanthellae like a little bit, not much, but a little N and P to color up and do well and a decent skimmer can get rid of other stuff.
I've used ATS in the past before getting into plants, and the plant filters got more and more interested.
But then why have a plant filter at all? Just make the entire scape and tank itself the filter.
Export is plant cuttings which you can give or sell. Inputs? I add nutrients, I'm not trying to export them, I'm trying to keep the levels up to help the plants grow.
Fish? I've bred maybe 50 species in planted tanks over the years.
Well, go ahead and play with the ATS's, but you'll need t prove these things to yourself over time. I had to and thought many of the same and similar things myself back in the day.
Cannot fault anyone for that, least I'd have to slap myself for doing it too
BTW, algae are not limited by nutrients in planted tanks.