At least according to the Wikipedia entry, in the early 1990s. No surprise there -- just about everything went wrong around that time, and has only gotten worse since. Those changes therefore require a few broad causes to explain them, unlike the proliferation of specific causes that everyone cooks up.
The over-arching one is the trend in the crime rate, although I don't see that working directly here. Falling crime does reduce creativity, though, which sounds right in this case. The junkier the composition, the more you have to rely on over-the-top presentation to make an impression.
I think you see that in a related way with how blaring the composition is, aside from how loud it's played live or recorded. Heavy metal from the good old days isn't overly busy or offensive to the ears (I mean Judas Priest, Iron Maiden, Scorpions, and so on). Once metal bands couldn't compose anything good, why not try to make albums that sound like Thor is farting thunder, the Devil is growling a tidal wave, etc. etc.? Same thing with swing music in the later '30s and early '40s -- absolutely, positively cacophonous compared to the sweeter dance music of the Jazz Age.
The '90s also seems to me the time when TV commercials got horribly loud. I don't remember people always muting commercials in the '80s. Same reason as with recorded music: those commercials were sincere and inoffensive ("This Bud's for you"), whereas the snarkily composed ones from more recent times need to be louder since we tend to tune out obnoxious sarcasm.
Nothing in the CD or TV technology of the '80s prevented producers from starting a loudness war, so it was either a change in the content of what was being recorded / broadcast, or a change in audience preferences. The content change is obvious. I was about to say I'm not sure that people like listening to loud junk, but then I remember how often you hear just that blasted out of a car stereo. Or how often you hear that in a mall or shopping center, where every store has their own awful music playing right next to everyone else's. It's not so bad that you hear it down the block, but still strolling along the storefronts, it's off-putting.
The one place I enjoy loud music (other than the obvious dance club) is supermarkets. They're the only place that sometimes plays good music, and it can be hard to hear it above all the rolling cart wheels, crinkling bags being pulled off of shelves, babies crying, and whatnot. The only wrinkle is that the supermarkets that draw penny-pinchers will frequently interrupt good songs just to blare some horrid pitch for UNBEATABLE BARGAINS.
It doesn't even have to be an expensive supermarket, just one that isn't trying to be an efficiency-obsessed hellhole. ("What a waste to play music on the PA when we could be hawking our deals!") Tonight I got to hear "Walking on Sunshine" and almost expected to hear "Tenderness" after -- well, some day.