Somone wrote:
"My second claim is when the mismatch condition at the coax destination,
i.e. antenna that may result in significant radiation from the coax
itself."

Responses already show this is untrue.

Radiation from the external coax surface comes from launching a signal
on that surface. Good coax does not let signals penetrate its shield.

A mismatch between a transmission line and its attached antenna affects
both transmitting and receiving from the antenna, but does not launch
signals on the outside of the coax.

A mismatched transmitting antenna does not accept all available power
incident upon it and reflects a portion back toward the sender depending
on how bad the mismatch is.

A mismatched receiving antenna has a source resistance (radiation
resistance) and may also have reactance. A conjugate match is needed for
maximum power transfer to the feedline. The mismatched antenna will
either not extract all the power available to it in the passing wave or
else reradiate more than 50%, (with full extraction, the minimum
possible reradiation is with a perfectly matched antenna). Consider a
short circuit across the antenna feedpoint. 100% of the energy extracted
by the antenna is reradiated. Consider an open circuit at the antenna
feedpoint. Little if any power is extracted from the wave sweeping the
receiving antenna.

The most power is received by a receiving antenna when its radiation
resistance is matched to the Zo of the feedline. In this case, 50% is
the best possible received carrier power in the receiver input. Nobody
tells the antenna it is a receiving antenna. It is a conductor carrying
a current, never mind where it came from, so it is going to radiate.
When matched resistances are involved in source (radiation resistance)
and load (Zo matched), the power is split 50-50 between source and load.
The radiation resistance, is the source resistance for the receiver
load, and it represents the reradiation from the reeiving atenna.

50% of the received power accepted by the load is the best possible
performance. Mismatch means less. Either less power accepted by the
antenna or more power reradiated by by the antenna.

A transmatch can make the feedline appear as a matching load at the
antenna junction for receiving. If matched for both transmitting and
receiving, all available power will be transmitted and received.

Best regards, Richard Harrison, KB5WZI