In which situations would it be beneficial to retain connected earth electrodes after a TT earthed installation is converted to a P.M.E. earthed installation?
Probably almost all circumstances it does no harm, - it is no worse than leaving the water pipes connected, indeed it may well become a requirement if the regs continue to harmonise, as it is already in many countries to have an electrode at any building on the end of a PME like supply.
Mean while it reduces the voltage rise during induced lightning events, and ties things down better for any kind of EMC that is too fast for the PME earth to be any good (a few microseconds per 100m of cable). It is also a good idea for radio equipment, for the same reason (at a few MHz and faster, anything more than a few percent of a wavelength away means you do not really have a connection at all.)
A standard UK rod, even in Essex clay, is no use for holding down a floating PEN, against any load more than a doorbell transformer so I'll not mention that, as I think it is a red herring, unless your electrode is several square feet of steel piling.
A TT earthed house that has two substantial deep earth rods had a E.F.L.I. of about 8 Ohms. I am inclined to retain the rods after conversion, especially after viewing the Virtual Elex presentation about P.M.E. earthing and diverted neutral currents.
