The main reason people do this stuff is because somebody came up with the idea mostly out of ignorance and everybody started repeating it so that it somehow became true. From there to becoming a fad it doesn't take that long, especially when the Internet comes into play. Just to set a couple of things straight:
1 - Beer carbonates faster the warmer it is. The speed at which beer absorbs CO2 is determined by the diffusion rate of CO2 in the beer. The laws of physics tell us that the rate increase with increasing temperature (more kinetic energy = more speed). Of course, since the solubility of gases decreases with temperature this means that we'll need to set a higher pressure in the headspace to reach the same amount of dissolved CO2 in the beer, but we'll still get there faster the warmer the beer is.
2 - Suspended solids drop faster the warmer the beer is. This is due to the fact that a liquid's density and hence its viscosity decreases with increasing temperature and it's the viscosity that determines how much resistance the droppping particles will encounter. Lower resistance = higher speed. Water has the so-called "anomaly of water" which means that below 4°C its density starts decreasing again. Still at 0°C density is higher than at 20°C so a warm beer will still clear faster than the same beer cooled to near-freezing temp. Chill haze is a totally different issue as it needs first to form and then to become permanent for it to start clearing at all. For that to happen you do need cold temperatures but on the other hand you also need to keep the beer cold for much longer than a couple of days, i.e. you need proper lagering (or cold-conditioning if you will) for chill haze to clear without filtration, if you just "crash" for a couple of days and then transfer the chill haze will still be there.
Cooling beer very fast also had the issue that the yeast will experience a thermal shock and go dormant. This could inhibit, among other things, flocculation and maturation of the beer (VDKs cleanup and all that stuff) which means your beer might take longer to mature or possibly have serious issues like detectable diacetyl.
I know I'm probably fighting windmills here but I'd still like to put that out, make of that what you will. Cheers.