The effects of loading on an output transformer and on a mic are somewhat different.
Particularly in the case of said Ampex machines, loading the xfmr had two roles, damping the HF response rise and ensuring the VU-meter accuracy, the latter being the most significant effect. Low impedance transformers do not have much HF resonance in the audio range.
Microphones react differently to loading.
Most active mics react to loading with just a little decrease in output level, sometimes with slightly increased distortion and reduction in max SPL, but no change in frequency response.
Dynamic and ribbon mics react to loading with a decrease in level AND changes in frequency response.
There is a change at the intrinsic resonance frequency of the diaphragm, where loading damps the resonance hump, and a change at HF, where the inductance creates a low-pass filter.
The global output decreases when such a mic meets a low impedance, by the mere effect of voltage divider.
Most vintage mic preamps took care of these issues by unloading the secondary, making the input impedance inductive, which resulted in quite high impedance at mid and high frequencies.
Most of solid-state preamps designed in the 70's and on concentrated on bench performance with dummy loads, which resulted in fairly constant but low-ish input impedance.
Cf Neve preamps with 600/2400 switchable input impedance.
It posed no problems with condenser mics, and dynamic mics were often considered inferior anyway. Ribbon mics were commonly accepted as "dark".
It's only quite recently (2000's) that the subject has been revisited, with in particular AEA that came with high input impedance that allowed them to demonstrate that ribbon mics were not as dark as commonly admitted.
Loading a mic with a resistor of value close to the nominal impedance brings no benefit in terms of EMI/RFI rejection, because whatever reduction in noise is accompanied with a similar reduction of global level, requiring increasing the gain.
With very few exceptions, mic manufacturers don't publish the effects of loading on their mics, but these effects are real, and significant enough to be heard even by untrained listeners, with a large majority voting for the highset impedance load..