Bob,
That baloney comes from
this site selling Kleen Pool. It's complete bunk. All algae are plants except for what is known as blue-green algae which is a cyanobacteria (bacteria that use photosynthesis). The color of algae is often the color of the chlorophyll which is what absorbs light for the algae to turn into energy to make complex molecules (i.e. to live, grow and reproduce). Algae is not a fungus and it does not require an algaecide to be killed -- chlorine kills it just fine, but the active chlorine level is based on the FC/CYA ratio so with high CYA levels it takes much higher FC levels to prevent algae growth.
If the pools where you've added copper-based algaecide are plaster pools, then be very careful to keep the pH lower (or the TA too high) or else you can get metal staining. Since these pools are Trichlor pools, their pH probably tends to stay low which is fortunate.
If you were to raise your target FC level as the CYA level climbs over the season, then you would help prevent algae. You could supplement by adding chlorinating liquid during your weekly visit as well. If you just want to live with the higher CYA and not raise the FC level, then there are several choices for preventing algae. Copper is effective, but can stain and turn blond hair greenish. Polyquat 60 can help but is not perfect and must be added weekly since chlorine breaks it down (somewhat slowly). Phosphate removers will often, but not always, work to take the edge off of algae growth, but can be very expensive if phosphate levels are high. Another type of algaecide is an ammonium product since that combines with chlorine to produce monochloramine that kills algae and does not bind with CYA, but this is a one-time solution, not an ongoing one. However, you could use chlorine alone (as tens of thousands of pool owners do on this forum) if you were to add unstabilized chlorine (mostly chlorinating liquid or bleach) to the pools more frequently, say with twice a week visits (make it a quick one and skip the brushing for the mid-week visit).
By the way, I live in the S.F. Bay Area in Marin County that has fairly tight water restrictions, but even there I use winter rains to dilute the pool water annually. As for water dilution, the largest pool service in our area that services thousands of pools still does partial drain/refill when the CYA level gets to 100 ppm and they usually target 4.5 ppm FC for their pools, though also add chlorinating liquid during weekly visits if the pool water is cloudy (usually nascent algae growth) or has visible algae. They don't follow the FC/CYA ratio (because they don't know it), but have learned through experience to target a higher FC and not get the CYA get too high, which is pretty much the same thing, just not as precise.
Richard
