Adding high amounts of chlorine or shock can often take care of the symptom of the problem - the algae - but it doesn't eliminate the source of the problem: nutrients.
The problem with relying solely on chlorine is that whenever the free chlorine (fc) drops and water conditions are otherwise right, algae will begin to grow.
By removing the phosphates from the water, you deprive algae of a critical nutrient thereby preventing it from getting established in the first place.
Chlorine is an important component of providing safe water for your enjoyment, however phosphate removal is key to preventing algae growth.
For a trouble-free pool... solve the root cause of the problem. Preventing algae growth is much easier than continually treating it.