With perhaps 100 AG bitters under my belt, I have always cooled the wort in the boiler overnight, I have never transferred the protein trub to the fermenter, I have never had a chill haze, and I have never had an infected beer.
I boil my wort in a 5 gallon Burco outdoors in an open-fronted garage. Once the boil is complete I top the boiler up to within a centimetre its rim with boiling water, put on the lid then seal this in place by wrapping cling film around the top of the boiler (half the clingfilm's width around the boiler and the other half folded down over the lid to form a seal).
This forms a vacumn seal which becomes tighter as the boiler cools. It's impossible to draw more than half a litre of wort the following morning without firstly breaking the seal.
I always aim to start brewing at around 2.30PM which means I switch off my boiler at around 7.00PM. I transfer the wort to the fermenter 12 hours later leaving all the detritis behind in the boiler. By this time it is cool enough to enable plenty of oxygenation and I then pitch my yeast straight from the packet.
I see one proviso in that because my boiler is effectively located outdoors the night air obviously helps with cooling and I invariably serve my beers at 13C which is the temperature in my cellar. However, for me it works every time, so I see absolutely no point in making things harder
