One thing puzzles me, why does it matter if a FET is put into
a circuit the wrong way around, with source and drain interchanged,
because a FET (JUGFET, MOSFET) is symmetrical in its construction?

Your "because" is too general a statement.

Some types of FETs are, in fact, physically symmetrical in
construction, and the source and drain are interchangeable. Most
JFETs are like this, as are "lateral" MOSFETs (the usual sort in IC
manufacturing, and some older audio power MOSFETs.)

However, the commonly-used "vertical" MOSFET is different... it's very
asymmetric in its construction.

https://electronics.stackexchange.co...ted-with-arrow
has a good set of explanations... including the detail that in a
vertical MOSFET, the substrate is normally shorted to the source right
at the semiconductor die, in order to suppress the "parasitic" BJT
which lurks inside the silicon structure.