Why not use a MOSFET instead of a BJT?

A mosfet requires usually a fair bit more gate voltage than the transistor ~0.7V so that's an immediate advantage. For a crude N-fet switch / emitter follower it also means that you've got that same ~0.7V voltage drop over the transistor instead of the mosfet >2V.

BJT is a current-driven device so the base will drain the line charge by itself even if there is no pull down/up resistor. Transistor base is also not bothered at all by a high voltage drive signal as long as you have a suitable series resitor in base. A mosfet will fizz if you connect e.g. 48V signal to the gate. Beware of the reverse voltage rating thought.

The transistor base current on the other hand is a source of many headaches if you are using a transistor as an inverter. That 60µA current is perfectly fine for lighting up a signal LED for example..

This looks like a power sequencing circuit to enforce some control between the 1.2V_HT and 5VPCU lines. The 10k and 0.1uF capacitor delay the 1.2V_HT signal a few milliseconds before the BJT starts conducting.

As @barleyman said MOSFETS need tend to need more voltage at the gate than a BJT, especially if it needs to operate with less than 1.2v. Common,cheap MOSFETS such as the 2N7002 (also used in this circuit) have threshold voltages that can be as high as 2.5V.