why does a desert cooler cool better in hot dry days

The short, simple answer is due to evaporative potential. The lower the ambient humidity , the more effective the evaporative coolers work. When water evaporates it takes heat energy with it. The more range between ambient and 100% humidity, the more heat energy the evaporation will dissipate. If the ambient humidity is at 95%, the evaporation cooler will only have 5% of cooling potential where as it will have 95% cooling potential of its only 5% humidity.