Normally, I see a pressure switch used to control the submersible well pump, to turn it on and off.
Would it be possible to just have the well pump controlled by the heat pump, such that when the
heat pump turns on, it activates the well pump, and when the heat pump turns off, it deactivates
the well pump.  This would eliminate the need for a pressure switch, right?

With the right pump you could do as you describe. Pressure switches and tanks were an attempt to keep pressures fairly static without short cycling pumps in low use situs (i.e. washing your hands).
With the relatively low pressure requirements of geo, low pressure or vari pumps have the advantage of low noise from flow raters.
J