I think I have mentioned some of this previously on this reflector site,
but I can summarise the points:
- a tuned counterpoise (when correctly tuned) could be thought of as
being opposite in phase to the top part of the antenna, so the electric
flux has an affinity to terminate on the tuned counterpoise rather than
return via ground (at neutral potential).
- as the ground is lossy, arranging for currents to return by low loss
tuned radials is indeed an efficiency gain
- I have seen diagrams of commercial LF tuners with tuned counterpoise
where the connection to ground is taken from a selected tapping point on
the loading coil, and selecting the tapping point for minimum ground
current is the same as the condition for maximum efficiency (and it may
need to be adjusted on-site, not predicted by theory).
- I'm not sure if it is valid to say that the antenna proper and the
tuned counterpoise form a net series resonant circuit, but that is my
personal view. I also suspect that separate tuning of the top part and
counterpoise, then connecting as a system, would generally require
complete retuning, due to the mutual coupling.
- In most amateur antenna situations (modest height and size), running a
tuned counterpoise is a nuisance for having a "trip wire". If the
counterpoise is supported at a safe height (above head height) it
probably detracts significantly from the effective height of the antenna
system, so may not be a total gain compared to no tuned counterpoise.