Telamon,

The objective is the impedance transformation.
-R- True

The voltage transformation is a result of the
impedance transformation.
-R- True - However for most situations the Voltage
Transformation is a good thing and another
benefit in using the Matching Transformer.

I've wondered about whether the input radio is responding
as a voltage or power sensing device. The answer is power
because the receiver input is low impedance so the
transformer is not changing the dynamic range of the
antenna/transformer/radio as power in equals power out
of the transformer.
-R- Yes - WRT the Matching Transformer Power "In"
and Power "Out" are the same. - It is MHO the the
'relative' Voltage Dynamic Range between the
Antenna-Side and Radio-Side of the Matching
Transformer does change. The Receivers Input is
Low Impedance - However IMHO it is the Voltage that
is being 'sensed' and processed within the Receiver
from RF to IF and then AF Power Ampified into an
Audio Signal.

A problem with the way some questions above are
posed is that there are not enough specifics defined
so I'll define them.
-R- True.

Let's say this is in regards to a long or a random wire
antenna. As a single element in the air it will function
as a voltage common mode antenna. This one element
is really half an antenna. For it to do useful work you
need an RF ground. You also have the problem of getting
the power it develops to be absorbed by the radio input.
-R- OK.

The voltage type transformer provides the impedance
transformation from the high impedance of the wire to
low impedance of the receiver input or coax of the same
value so the energy is transfered efficiently.
-R- The Key-Objective in using the Matching Transformer
is to 'match' the Impedance of the Radio-Side to the
Antenna Input {Impedance} of the Radio.

Now the transformer (UNUN) can be wired in more than
one way. One way is to use the radio ground, which is
in part the mains system ground as the RF return. This
is just fine to do as long as your local mains ground is
quiet in the frequency range you intend to use it. However,
this is not likely so you create a ground with the explicit
purpose of being the RF ground. This can be a ground
rod or radial wire on or under the ground routed under
the wire antenna.
-R- Yes - The selection and use of a Ground {Grounding
Point} can contribute significantly to the performance of
an Antenna + Matching Transformer + Feed-in-Line + Radio
System.

Another benefit is a static charge on the wire is shunted
to ground instead of through the radio input.
-R- True

To Re-State My Two Points :
* To my way of thinking Matching the Impedance
of the Radio-Side of the Matching Transformer to
the Radio's Input Impedance 'optimizes' Signal
Transfer from the Antenna {Ground} to the Radio.
* Plus reducing the Voltage Dynamic Range of
the Signals coming out of the Radio-Side of the
Matching Transformer 'feeds' the Receiver with
Signals that the Radio can more easily process.

it's just the way that i envision things - iane ~ RHF