The Cairo building was completed in 1894. After completion, it was the tallest building in Washington DC. During that time, in the US, skyscrapers and tall residential buildings were being built. However, given that the new trend had not been tested with time, congress as well as the public developed an uneasiness in regards to tall buildings stability and longevity. Therefore, the height of Building Act of 1899 was passed due to those concerned. The sentiment developed, projected an image of tall buildings being unstable, having a life span of 75 years, as well as difficult for firefighters to extinguish fires if needed ( let’s not that at the time, firefighter were just able to reach fires as high as 85 Meters from the ground).
After the Cairo was built, nearby residents lobbied congress to limit residential buildings heights in DC, they were successful in doing. Hence, the height restriction in DC. Unlike the common assumption attributing the restriction the Washington monument or the capitol building, the actual reason comes from the Cairo building.