Algae is a perennial questions on this forum. I don't mind it, and the fish eat the large stuff for me, but I know it can be a real problem with streams and waterfalls if you don't want the woodsy look. The people I know around here scrub it all down regularly. I knew one person who put chemicals in regularly to kill everything.
If you put clean water in a bucket outside here it will become slimy with bacteria in couple days. Then it will likely turn colors as the bacteria build up. Eventually that will die back and algae will form. Critters will lay eggs in the water and water snails appear out of no where. Life is amazing that way.
Any kind of nutrients in the water will encourage all of this. When you see a clear stream with no algae in nature it's because the water is extraordinarily clean (upstream plants and gravel have scrubbed it), it's fast moving, and there are constantly critters and insects picking over anything that starts growing. When you see a clear stream with no algae in commercial environments, it's usually been treated with harsh chemicals to kill everything. Homeowners often clean and scrub everything to remove visible algae. I don't know of any other truly algae-free environments.
All the stuff you're doing is right, though. Control the free nutrients, move the water around, remove mechanically. I'm going to have to defer to the others on the forum for cleaning tips and practical advice, though, since my ponds are more ecosystem than decoration.