This is with R=100ohm. You may see below the gate current is much higher (+/- 75mA in peaks) but it charges/discharges much faster. The gate current is most of the time zero..
Mind it is an simulation with a Mosfet model only, the generator is 25kHz 1:1, 10V, 100ns r/f edges.
Indeed, MOSFET gates aren't ideal capacitors by any means, the plateau is very evident in those traces.
In real life there's always ringing and other artifacts as well.