MOSFET gate inrush current
The gate driver can only sink a few mA (maybe as much as 20mA with a 9V supply) and can only source at most about 100uA so it's unnecessary.
This kind of driver is only suitable for very slow switching. Milliseconds in the case of turn-on, because that charge pump is really wimpy. Say the internal capacitor is 30pF, a rather large capacitor for integration on a chip. It only operates at ~80kHz so it will only be able to supply a very small current. Q3 is another matter, but you can tell from the discharge times that the typical current is quite modest.

A driver that can sink or source amperes such as the TC4420 is much more likely to need the on/off times extended.
Of course there is nothing stopping you from adding an external resistor if you want to make it even more glacial in response time.