With a typical TCR of 50ppm and a perfect tolerance, the resistance value will shift 0.25% at a temperature rise of only 50℃. This shift could be on either side depending on whether the TCR is positive or negative. Another way to think about the situation is that if the design criteria calls for a resistance tolerance of 0.1% then to remain within the design limits you should specify a 10ppm or better TCR.
An example of an application where this may be important is the measurement of mass. This is typically accomplished using a scale. Scales may be used to measure the mass of gems, pharmaceuticals, or even larger items like construction equipment or bricks. Whether the scale is in a laboratory or located on a shop floor it is important that the instrument be accurate and consistent regardless of the environmental temperature. Most scales operate use the principal of a Wheatstone bridge.