A point to add about using an EQ is that any additional devices added to the string of amplification will also add additional noise. The fewer devices in your system, the cleaner the sound will end up being.
Your absolutely correct Sir.
And that is the reason, that if someone is contemplating, the purchase and insertion into their audio system`s signal path a equalizer, the selection of the equalizer and it`s performance/specifications should be carefully chosen to minimize any undesirable artifacts into the sound.
Most, if not all, consumer, and some "pro" grade analog equalizers are fairly crummy in design, in the noise, distortion, etc. specs
Quality(expensive) analog equalizers, not only are very low noise, distortion, but are also minimum phase, and importantly they are a combining filter type design, and when the audio system is properly equalized/voiced/tuned, by reducing the room`s node`s/speaker response peaks, then there is no additional gain(noise) added to the system and their insertion SQ can be transparent.
Only replacing the loss in overall system`s signal level with the equalizer`s level control for level matching non equalized to equalized for the proper original system`s signal to noise ratio
No boost should be attempted, and if not done so, little to no additional artifacts will be added to the signal chain, and that`s where people tend to screw up equalization by boosting(chasing ruler flat 20H to 20 kHz), thus helping to give equalizer`s a undeserved bad rap by misapplication.
You may not have known it but, as an example, all those movies that you liked in the big mono-plex theaters that you watched in the fifties through the eighties, or beyond(don`t know after1981, as not been to one since) were highly likely carefully equalized to greater or less extent with Altec passive cut only equalizers with adjustable line amps to return the signal path level from the room`s node`s/speaker system notch filter/s insertion loss.
Many others, and I have heard many decent, through HQ sounding audio systems improve in smoothness/tonal balance and long term listenability at all SPL listening levels, from proper equalization.
Peace, and kind regards, OKB