I have never used high light and CO2, so my comments are of a general nature. But whatever the method, low-tech (natural) up to high-tech as here, the principle is exactly the same: balance between light (intensity and duration) and nutrients. If these together provide what the plants can use during the photoperiod (duration), algae has a disadvantage. But as soon as light extends beyond the available nutrients, algae will have the advantage. And in this balance, the plant species and number must be factored in as well, since different plants have different needs.
For example, here we have Java Fern and Anubias which are low light requiring plants, and thus low nutrient as well. These should be grown in shade, such as under floating plants or under overhanging larger plants like swords. But there are also some higher light requiring plants, such as the Wisteria, hygro, microsword, and aponogeton. Working out the balance with light for provide for these differing needs can be tricky.
To algae for a moment. No tank can be free of algae, if it is biologically healthy. But we aim to keep algae under control by balancing the light and nutrients for the plants. The wood in all my tanks is covered in brush algae; but it is not present on plant leaves. When I saw it increasing on the plants, I jigged the balance until it stopped. It is a bit easier for me, as I do not have any high-light requiring plants and I provide moderate light with floating plants.
Byron.