"Over compressed music" already sounds like ass, it won't be changed it'll just be quieter.
OTOH, "Under compressed music", IF it's going to get turned up to meet the same average, will have to get squashed down in order to not peak over 0.
I don't get why you think "under compressed" music will have to get squashed (aka compressed)...?
The LUFS standard algorithm is not applying any processing at all...just a level change..from what I've read.
But you are right, the over compressed music will be much quieter, and due to it's flat-line nature of little to no dynamic range...it won't just be quieter, it will sound "smallish" when compared to the dynamic stuff that gets it's overall level raised so they both have the same relative loudness.
I think you can easily even test that in your own studio setup...just find some really crushed music that's out there...and then take a more old-school dynamic mix...and set them both to what sounds to be about the same overall perceived loudness to your ears...and then A/B them...I'm pretty sure the dynamic mix will sound louder/punchier.
TBH...I'm happy to see this change coming...because when I take my mixes and apply some basic level boost, just to get it a bit louder...it's still not close to some mixes I've heard from people...here and elsewhere.
I can easily match their loudness...but at that point, I hear my mix level balance change, the tonal balance change, and the dynamics shrink...which I never really cared for, but at the same time, felt that it was necessary to make it sound competitive.
Now that will not ever be needed....and while there will be holdouts, who don't use these streaming services...I think over time, the broader music listener base will reject those, because they will have been "retrained" to appreciate the more dynamic mixes at more reasonable processed loudness (less compressed).