There is a downside.
If the current is too high, you lose the linearity of micro-stepping. If the highest current exceeds the maximum, then the highest current micro-stepping positions will collapse on each other.
If you are within the specs of the motors, there are no motor-related problems caused by higher currents.
But other problems can be caused by increasing the current. The current must be within the capacity of the motor drivers and their heat sink. If the drivers overheat, many will simply shut off, causing the motors to not move when they should, which will appear as misalignment on X, Y, or Y.
Another problem could be higher vibration, which would show as stronger ringing when going around corners. The higher current will give higher torque and higher acceleration, which will cause more vibration.
If you are increasing the current to support a bigger and heavier print bed, you will possibly have other troubles. Although the higher torque will be countered by the higher bed mass, the higher bed mass may be coupled with longer belts, which will be more stretchy. You may also be imposing forces over longer frame components, which may cause them to flex more.