Accelerating charges (electrons) radiates. AC current is accelerated charges. It radiates of power. Any hunk of wire that you push current through radiates. The only questions are how well and in what direction. Single-wire antennas will have radiating current through the "antenna" ... and radiating current on the feedline, the transmitter, nearby conductors ... all over everywhere. This is not necessarily bad. For instance, a quarter-wave inverted-L antenna, working against earth ground, fed with 50 ohm coax, is just fine. The current from the feedline center conductor goes up the antenna wire. The current to the feedline outer conductor comes from the ground stake or counterpoise or radial system. These are equal currents. Equal concentric currents on the coax feed don't radiate, so the feedline does what it's supposed to do: carry an electrical signal from the rig to the antenna where it will be radiated. Now let's look at the end-fed half-wave wire, worked against the feedline ... an end-fed Zepp, for example. Figure 3-2 shows a typical structure. The current into the end of the radiator must be equal to the net current down the feedline. As a transmission line the "differential" currents must be equal through each conductor in the line. But there is a "common mode" current down the transmission line too, caused by the antenna wire hanging off one side "unbalanced". The feedline is made of wire and can radiate too. What makes this work is the fact that if the radiator is a half-wave long, there isn't much antenna current in common mode that causes the feedline to radiate too. In fact, that current is usually only a few percent of the feed current. This method is used more often than you think. The common J-pole is really just an end-fed Zepp with a shorted quarter-wave feeder, tapped to get a good match for 50 ohm coax ... usually mounted with a vertical half-wave radiator and a vertical quarter-wave feeder. The Cushcraft Ringo is a commercial example, using a tapped L-C matcher.
The antenna sketched in Figure 3-3 B seems like a good way to drive a longwire antenna with coax. To remove any last radiating currents from the feedline, a "choke" balun might be placed in the feedline, or maybe its braid can be "earthed" so there is very little common mode current on it by the time it reaches the shack. Earthing it a quarter wave from the feedpoint, or three quarter wave will probably have the least effect on the feedpoint impedance.
The idea of terminating a longwire in a few hundred ohms is a technique used in Beverage antennas, Vees, and rhombics. The idea is to make an antenna that does not have a standing wave current distribution on it, but has a more uniform current along it. These antennas tend to be more unidirectional. These traveling wave antennas have current from a feed entering one end of the wire and current leaving the other end of the wire and going through some load resistor. A single-wire over ground is a Beverage. Two wires fanned out make a Vee. If the wires are bent back and fan in as to a termination, the diamond-shaped antenna is called a rhombic. If these are terminated at the far end, they are unidirectional. If the far end is left open, they are bidirectional. Placing the termination in the wire a quarter-wave from the far end allows us to use a structure that is not close to the earth. The feed can be coax a quarter wave from the near end, as suggested before. The disadvantage is that we now have a single-band antenna ... the lengths are only a quarter wave at one frequency. But the impedance matching can be handled by a tuner, so things may not be too bad.