Your AGC wasn't working correctly

You can't say that without seeing the setup. There AGC can only cope
with a certain range of signal and can't do miracles. I proved the
signal level was too high by putting in one (and two) 40db attenuators.

80db of amplification needed to be attenuated? I'd like to see an
amplifier with that type of gain.

A TV should work just fine within a quarter mile of a TV transmitting
antenna. The induced voltage at that point can be handled by the
AGC circuit and that voltage is much higher than the best amplifier
can produce from a weak signal.

Without even knowing the type of amplifier I was using or its design,
you cannot say that it doesn't add a lot of noise. Noise is not a
"distortion product".

I said "good amplifier".

Whether the noise is atmospheric, molecular, IM, or anything else, a
"good amplifiers" benefits far outweigh its "noise".