There is something about thriving healthy plants that drives away algae. The more the better.
Im not sure anyone can explain why, alleopathy is one hypothesis but the jury is definitely still out. But you are right, for whatever reason it has little to do with "out competing algae for nutrients" as so often gets stated.
Any condition that is unfavorable for plants can encourage algae. That includes not having enough light for whatever species.
Just like nutrients, it is impossible to "starve algae" by reducing light past the point that it becomes unhealthy for the plants. Algae doesnt need a lot of light (or nutrients) in the first place.
A tank full of high light plants struggling to grow under 25 PAR can get algae just as easy as a tank full of low light plants under 150.
(I consider mulm a nutrient)
In a high tech set up, decaying matter and dirty conditions promote algae. Clean conditions deter it. Frequent water changes are a formidable weapon. Plants love it and algae hates it. General good tank husbandry should be the first thing addressed when facing algae issues. One of the main causes of algae is neglect. Not saying yours is neglected, just making a point.
Instead of looking at it like a battle against algae, focus on what the plants need to be at their best, and the algae problem will usually take care of itself.