The first time I heard "When you hear hoofbeats, think horses, not zebras" I was appalled. How about we just empirically determine where the hoofbeats are coming from before eliminating the killer zebras as a possibility?
Because we have limited resources, time and every intervention can cause more harm. For example, you don't want to get an MRI every time you get a headache - it would be counterproductive to you, drain resources from a system which needs to handle more patients, and regularly make you visit an environment with potential infectious diseases. Where we have a quick and simple empirical test, we often apply it and the available options are growing - for example we have quick tests for a number of respiratory diseases, which wasn't available earlier.