There are many different reasons why most experts now recommend a longer turf grass. Here's just a few:
Promotes longer root growth
Provides shade to soil beneath, which reduces weed germination
Reduces chance of drought conditions forming
Cutting too short damages it's ability to sustain continual growth
Longer Root Growth
More and more evidence has come out directly connecting longer grass blades with it's ability to handle larger/longer root systems. The healthier the root system, the healthier the turf grass. Developing a strong plant infrastructure/root system is key in a healthy turf situation.
Providing Critical Shade to Soil Beneath
If your grass is too short the sun can absolutely scorch the soil. This can severely hamper the turf's ability to thrive because weed germination takes off in that sort of situation.
Avoiding Drought Conditions
Cutting the grass too short can really increase the possibility of drought conditions forming. When the grass is too short the combination of all the negative effects can lead to drought conditions. Those are tough to deal with so it's best to avoid if possible
Damaging the Grass
If you cut too short you'll damage the overall turf to a point where it can't properly sustain new growth. No more than a 1/3rd of the grass length should be cut at any given time.