Would a four terminal mosfet work equally well if the source-drain polarity were switched?
It would be possible to construct a four-terminal MOSFET that was symmetrical, with source and drain indeed being interchangeable.  On the other hand, even with a four-terminal device, a non-symmetrical shape may allow performance in one direction to be improved beyond what would be possible with a symmetrical device.  A MOSFET integrated onto a chip will often have a gate which is confined to a single plane above the active channel, but power MOSFETs have much more complicated three-dimensional structures which generally favor non-symmetrical designs.