The gate does not conduct DC current.
But it controls the FET by its voltage (gate voltage).
To change the gate voltage, you need to charge gate capacitance (gate to source/drain/channel).
This charging is done through gate resistance / metallization.
Too high gate resistance leads to slow switching, which is bad for many applications.
It also causes many other bad things - like large gate (thermal) noise, low Q factor in MOS capacitors, etc.
Also, gate resistance is just one number, and does not reflect well the distributed properties of the gate network - which may be causing non-uniform gate delay and gate switching, hot spots, and other parasitics effects.
In particular, too large gate resistance will cause a dynamic gate opening due to drain dV/dt effect.
Note that sometimes, too low gate resistance is bad too - it may cause too large charging current, that can burn the gate network interconnects.