It depends on one's goal... If aesthetics are the most important factor in owning your pond, then the addition of a dye may be worth the detriment to fish production. As is the case with nearly all the food chains in the world, the food chain in your pond starts with the energy of the sun.
Phytoplankton are agents for "primary production," the creation of organic compounds from carbon dioxide dissolved in the water, a process that sustains the aquatic food web. Phytoplankton obtain energy through the process of photosynthesis and photosynthesis requires sunlight to occur. When you add dye to your pond, you reduce the amount of sunlight reaching the water and thus, reduce the productivity of your pond in producing phytoplankton. So by adding more dye than recommended, you have reduced that much more sunlight from penetrating the water.
Phytoplankton are also crucially dependent on minerals. These are primarily macronutrients such as nitrate and phosphate. This is why liming and fertilization leads to more phytoplankton as well. Submerged aquatic vegetation can out compete phytoplankton for these resources and this is often why ponds with a large amount of submerged aquatic vegetation are quite clear.
If one wants their pond to be naturally its most productive, they should not dye it, work to keep submerged aquatic vegetation to a minimum, generally in the 20-30% range depending on certain management goals and ensure their pond is not overly acidic with good amounts of dissolved minerals.
