Having been in the industry over 8 years, I'm almost embarrassed to ask, but it's something that been bugging me:
Considering that pressure/energy loss is almost always undesirable, and the fact that they're not easily pigged, why and under what circumstances would a reduced port ball valve ever be a better choice than a full port valve?

A well defined problem is half solved.

Full port cost more, and lots of applications don't need them. Installations like domestic water service (especially commercial & residential), many compressed air lines, isolation valves for steam traps, etc.

When only considering pressure drop and the ability to pig the line, there is no benefit or justification to use reduced bore ball valves.  The diameter of the hole through the ball determines the required OD in order to have full contact around the seat when shut.  Usually, the diameter of the waterway is around 60% of the ball OD.  So, the ball OD for full and reduced port valves cannot be the same size for a given valve size.  Said another way, the ball OD for a 3 inch full port is much larger than a 3 inch reduced port valve.  Because of this, manufactures cannot not use the same castings for full and reduced port.  A larger body is needed to enclosed a full port ball, so there is more material, more machining time, heavier valve, more cost.  In addition, the valve operating torque is a function of the ball diameter cubed.  So a larger, actuator is need for the full port valve.  The weight of a full port valve with actuator can be up to 600% more than a reduced bore valve.  The cost goes along with the weight increase.

Now considering cost sensitive general services such in HVAC chilled water, city water, instrument air systems, etc. where many decades ago, used globe valves (high pressure drop, but tight shut-off) or suffered with leaking gate valves (low pressure drop, but leaked), the cost and performance benefits of using reduced bore ball valves was huge.

Because of the cost difference, significantly more reduced port valves are sold than full port (by a factor of around 3:1).  This fact says a majority of valve applications can live with the increased pressure drop.

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