One rule of thumb about this is that if you have an above ground pool of 5,000 gallons or less it is almost always worth dumping the water and starting over, and otherwise you are better treating the pool. However, as others have already mentioned, there are many factors that come into the decision. For a larger pool, 15,000+ gallons, it is nearly always better to treat the water.
Some other factors that haven't been mentioned: If you replace the water you will at a minimum need to add CYA, and probably balance some other levels as well, which adds to the expense. In-ground vinyl liner pools and fiberglass pools can be damaged if drained completely. Replacing water is no guarantee of getting rid of algae, which will sometimes/often come right back as soon as the pool is full again. And so on.