In ???? some scientists set out to prove excess fertilizer caused algae. When the numbers where in the amount of nutrients in the water did not matter, the amount of active plant biomass did and in fact plants grow until the run out of nutrients, if they don't stop neither will plants.

So, when we remove them, if the nutrient load is the same, you now have algae.

We thought for a long time plants would simply out compete algae but that's only a small part of it, active growing plants change the chemistry of the water column, peroxidases from their chemical reactions (which, by the way is why barley straw works for pondkeepers to kill algae, complex organic peroxidases evolve from the soaked straw, this is not the same as adding hydrogen peroxide by hand) puts a serious dent in algae. For decades the way to not get alage, the only one that really works is "have fast growing stem plants" (Tom Barr) and "have 30% of the surface covered in fast growing plants" (Karel Rataj).

An easier way to understand this is people who maintain lush planted tanks such as aquascapes may keep adding Nitrate to keep it at 20 or 30 parts per million (ppm) while somebody else might be panicking because they have 15 ppm and the tank is all green.

Why is there no algae in the tank with twice the level of nutrients? Because there's a lot of fast growing plants (or a lot more slow growing plants, it's just a numbers game)

A quick search shows a snippet from the US EPA that explains it pretty well:

The Problem | Nutrient Pollution | US EPA
https://19january2017snapshot.epa.gov/nutrientpollution/problem
Dec 5, 2016 - Nitrogen and phosphorus support the growth of algae and aquatic plants, which provide food and habitat for fish, shellfish and smaller organisms that live in water. ... Too much nitrogen and phosphorus in the water causes algae to grow faster than ecosystems can handle.

That says it all, I think.