As already explained, the discussed driver circuit exceeds the MOSFET Vgs,max rating and also involves large power dissipation.
On the other hand, driving the gate of a 20 kHz switcher with 100 ohm driver impedance brings up some switching losses due to slow switching. The driver topology is simply unsuitable for a MOSFET switcher. You want a driver impedance below 10 ohm, reasonable gate voltage level of 10 to 12 V and low static power dissipation.
If using discrete transistor drivers, a NPN and PNP transistor for a complementary voltage follower should be afforded, also gate voltage adjustment respectively limitation.