Turn off MOSFET with diode - PWM controller Maximal output current
No need to worry about the driver, it will not sink more current than its own abs max regardless of how little impedance you have to the gate.
The part is designed to drive FET gates without the user having to worry about the peak current due to the gate capacitance.
It's the internal driver circuitry that limits the current, not the external components connected to the gate.
Update with examples of designs where no gate drive resistors are used (albeit with different controllers from TI) See here. And here and here.
And finally from the datasheet:
OUTPUT is the gate drive for the external MOSFET. OUTPUT is the
output of the on-chip driver stage intended to directly drive a
MOSFET. Peak currents of up to 1 A are sourced and sunk by this
pin.
The only discussion in the datasheet of a gate drive resistor is the trade off between switching losses and EMI.  There's no reference to a need to limit the driver current.