Current sense resistor using PCB tracks
The two main drawbacks are accuracy related: initial tolerance, and temperature coefficient.

Initial tolerance

PCBs are made to loose tolerances. The copper thickness is nominal, not accurately controlled. Even the etch width is subject to large variations. You might achieve 20% cross-sectional area accuracy to start with if you're lucky, much worse if you're not.

Temperature coefficient (tempco)

Pure metals have a steep tempco, copper is 0.4%/C. That's a 10% change in resistance for a 25C change in temperature. Resistors are made from alloys which have been designed to have near zero tempco.

For detecting whether a current is flowing or not, or perhaps even for the current sense element in a current-controlled converter where it's within a feedback loop, it might be OK. For measuring anything with any semblance of accuracy, use a discrete current shunt resistor.

A discrete resistor will have much higher power handling than a track. And if you should overload it catastrophically, it can be replaced, whereas losing a track would trash the board.