Beliefs are flexible. Physics is not.
There are two parts to reality: what we believe, and what the circuit is actually doing. A person can believe a thing is true or false without knowing which it is. Physics is less interested in the debate. It quietly keeps the receipts.
RF is alternating current at radio frequency. The voltage and current reverse direction over and over again. For power to move through an antenna system, there must be a complete path: an outbound current path and a return path. The exact distribution is not always neat, visible, or the same from one installation to the next, but it is never optional.
So where did the return path go?
With an end-fed half-wave (EFHW), the matching transformer couples the transmitter to a wire that is often operated near a current minimum. The antenna may still work without a separate counterpoise, but the return current still needs somewhere to go. With neither a counterpoise nor an effective common-mode choke, that path is the outside of the coax shield. The coax has just been drafted into the antenna system, carrying common-mode current.
Once that shield is carrying RF, the coax—and often the radio chassis and station gear—become part of the antenna system. That means you are exposed to RF from the coax and radio while operating. It is an unsafe and unnecessary way to run the station: the antenna has brought RF right into the shack. Give the return current a planned path instead.
Skip the counterpoise and the return path does not disappear; the coax, radio chassis, station wiring, nearby conductors—and sometimes the operator—get pulled into the antenna system. The coax has joined the club. The operator was not supposed to be a member.
Give the system a planned return path
The practical answer is not to scold the coax. It is to design the whole antenna system. A counterpoise of an appropriate length and arrangement provides a deliberate return path. A common-mode choke near the feed point helps keep the outside of the feedline from becoming an uncontrolled part of the radiator.
For additional margin, it is often sensible to add another choke near the radio. Around here the philosophy is: choke twice. Put one choke at the feed point and another near the station. That is not a magic phrase or a substitute for measurements—choke impedance must be adequate on the bands you use—but it is a very good habit of mind.
A small but important safety note
Unwanted RF on accessible metal, feedlines, or station equipment can create interference and, at sufficient field strengths, an RF-exposure concern. Exposure is a question of power, frequency, antenna geometry, distance, duty cycle, and time—not a universal prediction from one antenna label. Keep people and pets clear while transmitting, use properly rated components and enclosures, and evaluate your station against the applicable RF-exposure limits and electrical-safety guidance.
You cannot change physics. You can change your mind, improve the return path, and make the station more predictable. That is usually less dramatic than a head slap—and much more useful.