<p>Practical superconducting nanowire single photon detectors (SNSPDs) demonstrate a strong trade-off between detection sensitivity and the reset time. Often, there are wide variations in sensitivity and response times from SNSPDs of the same superconducting material. Here, using detailed two-temperature model incorporating both photon pulse and joule heating, we show that the dirtiness in a superconductor enforces a sensitivity and bandwidth trade-off in all practical devices. More importantly, a certain degree of dirtiness is a necessary requirement for achieving single photon detection. Under typical bias conditions close to the transition setpoints, the minimum number of photons required to register a voltage pulse decreases by the dirtiness parameter (Ioffe-Regel parameter) and the reset time of SNSPD increases by the same dirtiness parameter, thereby giving a constant value for the sensitivity-bandwidth product. The constant is weakly modified by biasing current and the temperature. Since dirtiness in the superconducting nanowire is a physically controllable parameter with an important bearing on the final response of an SNSPD, this work opens new opportunities to develop SNSPD devices with engineered sensitivity-bandwidth setpoint as dictated by an application.</p>