First, explain what you mean by "reverse EQ to your equal loudness contour". And to your final sentence: I am admittedly no Dick Cavett, so it might be my choice of words.
I mean you would EQ your system to make test tones equally loud to your ear at all frequencies. something many people at one point in their audiophile trip, have thought would give them neutral music. just to be utterly disappointed with the actual result.
to try and clear the air:
-1/ why 1khz? apparently... reasons, and likely because it's a nice arbitrary value that most gears could get right(remember those are stuff for manufacturer specs, it's as much marketing as it is objective data). it's not enough to assess to the actual fidelity of much of anything so it doesn't matter all that much if it's at 1 or around 3khz.
-2/ is the equal loudness contour significant in audio? of course. it's how we ear, so there are plenty of reasons to care about it.
-3/ is the equal loudness contour affecting how we hear at different listening levels? of course. and when I listen quietly, I have an EQ with among other things, some more low and high end boosts. but only because my gears are already EQed to what I estimate to be close enough to my perceived neutral at normal listening levels. without that assumption that we already are neutral at another listening level, the change becomes irrelevant. and my initial way to set up neutral on speakers(I take speaker to avoid HRTF right now but we can come back to that if you like with headphones), is through objective measurements and fine tuning based on subjective impressions. which seems to both align fairly well instead of my subjective perception of neutral going toward a perceived equal loudness contour. and that is so for pretty much anybody for perfectly objective reasons. basically our brain is calibrated to think that the way our hearing changes all sounds, is how the real world sounds like. so it applies to real life sounds from people talking to speakers playing a song.
-3.1/ now if you calibrated your speaker at 95dB SPL and you listen to music at 60dB, sure you probably should boost trebles and subs to feel a more neutral sound in general. but that is only because you have basically failed to properly calibrate your system to your listening habits. which is a very specific issue. not a general demonstration that we want less mids because we're sensitive to it, while missing how everybody is always more sensitive to mids all the time, including the guys making the song and the guys playing the instruments and singing, and of course, us listeners. there is never a rupture in that chain of flawed hearing that requires compensating for. at least not based on average curves. the variations we may need to address are individual variations in HRTF. which again is another issue compared to what you seemed to talk.