Since the RRR can vary quite strongly for a single material depending on the amount of impurities and other crystallographic defects, it serves as a rough index of the purity and overall quality of a sample.
RRR is also important for characterizing certain unusual low temperature states such as the Kondo effect and superconductivity.
This shifts the intercept of the curve to a higher number, giving a smaller RRR.
In practice the resistivity of a given sample is measured down to as cold as possible, which on typical laboratory instruments is in the range of 2 K, though much lower is possible.
By this point the linear resistive behavior is usually no longer applicable and by the low temperature ρ is taken as a good approximation to 0 K.