Anyways let's start at the spore level where it all begins
Spores can only eat ammonium.
No free ammonium no algae.
Sources include leaky plant tissue,bacteria decomposition ect
Ammonium, albeit at a very low level, will be present in the tank water all the time for the very reason you mention - leaky plant tissue, bacteria decomposition, etc. And algae spores utilize this for growth. Algae (and cyanobacteria) also need iron in the water column. And, photoreduction of ferric iron to ferrous iron ensures a supply of this element. Photoreduction occurs at wavelengths below approximately 500nm and that's why spectrum matters.Green algae has basically the same photosynthetic system as higher plants so why would you think spectrum matters?