Let me try to summarise.

A simple thing like a balun does only two simultaneous things.

It changes the impedance presented to the receiver (or transmitter).

And, because it disconnects the usually slightly radiating feedline from the
antenna, it changes to some uncertain extent the antenna's directional
properties both locally and at a distance.

On receive, the change in impedance matters very little. It doesn't matter
very much whether the impedances involved are 600 or 300 or 50 ohms. They
are quite arbitrarily decided by the mechanical construction of the
transformer and are arithmetically derived by (often wildly incorrect)
assumptions of values for line and receiver impedances.

The change in the antenna's directional properties sometimes, but not always
matters. It depends on the local environment and can affect such things as
signal to noise and signal to interference ratios. But you never know until
you've tried it.

The very general moral is - if there's an improvement in performance in any
respect due to fitting a balun then keep it. If there's no improvement then
you could leave it where it is or try to sell it back to the manufacturer.
It will seldom degrade performance.

On rare occasions, fitting a balun can make matters worse. But once again
you'll never know until you've tried it. And the "made worse" circumstances
are never reported in magazines. This causes bias in the statistics.

It can hardly be called "engineering". But there's nothing else one can do
in the presence of inevitable large uncertainties in the local environment.
It's this piquancy which adds to the pleasure of both amateur and
professional radio.

Professionals who have to earn a living play safe by predicting radio paths
to be typically within plus or minus 15 or 20 dB. Amateurs have the time to
spare to quibble about minute fractions of S-units.

And balun and antenna salesmen have no alternative but to hover around and
attempt to make a living out of the suckers. Everyone has a right to make a
living.
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Reg, G4FGQ