The "ground" has several effects on antennas, most of them negative (see e.g. Why does an HF "monopole" need dozens and dozens of radials while a VHF/UHF "ground plane" antenna only needs four?). In most cases the further away the whole antenna system can be moved from the actual (physical earth/soil) ground level the better its radiation efficiency and pattern becomes. Yet many amateurs are also led to believe that a "good ground" is something to strive for, not just for the actual electrical safety and lightning protection reasons.
For me this comes to a fine point in the "random wire" and also "end-fed half-wave" antenna guidance. These antennas — at least supposedly — involve feeding only one element at its extrema, using a transformer "matchbox" to compensate for the impedance at that otherwise unlikely feedpoint. But the question then becomes: what to do with the "other side" of the coax, or rather the "unused" side of the transformer windings.
The typical stipulation is that one "needs" some sort of counterpoise (which I'll note is often labeled: "optional"). There's all sorts of diagrams, some involving a second wire as long as and placed in parallel the main antenna, some attaching an arbitrary collection of scrap wire, others suggesting a short lead to a long ground rod being sufficient — and most admitting both that the counterpoise is something of a "stretch goal" and that RF currents will end up on the coax shield regardless!
What was most confusing to me is Palomar Engineer's End Fed Antenna guidance which very explicitly admits to this "common mode current" problem but yet also intentionally encourages the user to put the choke as close to the radio as possible.
The clear intent is for some sort of counterpoise to take up RF current on its own, but what's not clear is why this is necessary. What is clear is that it doesn't seem very desirable, since despite the pretty diagrams this seems to be a classic case of "allowing the coax to become part of the antenna". My reading of Cebik (W4RNL/SK)'s Counterpoise? On the Use and Abuse of a Word (PDF) article confirms my suspicion here but does not propose any particular remedy.
Is it actually possible to "end feed" an antenna? What if I abandon the advice to let my coax be part of the antenna, and put a common mode choke right at the matchbox? This would hypothetically confine the Actual Antenna Part to just the Intended Antenna Part — but then what becomes of the other wire coming out of the transformer? I don't want to add any other elements to my antenna, yet folk wisdom says I need some sort of something to "pull electrons from" attached to the counterpoise lug! Would a capacitor or some sort of resonant circuit inside a shield or even just a volumetric chunk of low-resistance metal be useful here?
