Who knows what causes the black algae to end up in our birdbaths but once it's there, it seems to be there to stay. I've got a bunch of birdbaths here and if I leave for a bit and come back I seem to have all the major color groups represented in my birdbaths and ponds and water features. I suspect birds carry the spores from water feature to water feature and if conditions are favorable for their growth (high temps, poor circulation) they bloom. Never really checked into where it comes from but we're dealing with spores here so they could be coming in on the wind.
One thing I know is that the algae doesn't cause disease. But, it turns sunlight and carbon dioxide into food and creates nutrients that help bacteria thrive. It's the resulting bacteria that is the problem. Algae harbors pathogens. The pathogenic bacteria isn't exactly harmless, think coliform bacteria as in e-coli. This is one reason why I have been religiously scrubbing and bleaching my birdbaths. Although lavender and daylily leaves may or may not keep the black algae at bay, doubtful they can kill off those types of bacteria.
Good explainer here of why black algae is so hard to get rid of-
Black algae is a very common type of algae, and is the most difficult to remove once it has formed. A colony of black algae always forms on the pool surface, and usually is first visible when it is about the size of a small fingernail, but can grow rapidly and eventually become larger than a dinner plate. The spores settle in a porous surfaces, such as Tough plaster (mostly caused by Calcium buildup), and begins to anchor itself to the surface. It is able to dig a root into the porous surface and from there can develop an extensive root network beneath the pool surface, usually between the plaster and the concrete. Once the root has been formed, the algae become visible, but at this time it is already too late. Destruction of the visible portion is by no means a guarantee that the entire colony is destroyed.
The black algae I get in one birdbath has been particularly hard for me to deal with. We're talking major elbow grease to keep it at bay since it's taken root in an older concrete birdbath that is pitted from the elements. I presume I've never gotten the roots regardless of how much scrubbing I've done so it has been coming back to haunt me. I once tossed in a copper product out of frustration and then though better of that and took the basin off to soak it in a kiddie pool for a bit. I don't know about other products because I've not used them for black algae or green algae or yellow algae or that rusty red crap that ends up in two of my bird baths that isn't really an algae. I was never comfortable with what I read on the labels when checking out products so I didn't buy them. Don't know about the enzyme products being marketed.
I never could get my hands on the G4 products that were advertised in the UK or the Cromelin or Bondall products used by the Aussies so I gave up and ordered the Hecht Neoprene product-
I'd search for a more affordable product if I were you. It's got to be out there and available in a quantity for a few birdbaths however I didn't have the time to keep poking around on the Internet. The only reason why I bit the bullet and bought the Hecht product was because I've got 10 birdbaths here not 9 like I originally counted, one small concrete pond, one concrete water feature, and oodles of ornamental concrete planters that I'm growing everything form cucumbers to bell peppers and rhubarb in. I wanted a product that was as safe as possible for the birds and for us to seal off all the concrete around here.