Back on topic...
The reason why you don't see it typically done with an ice bucket bath, with the hot wort going through the IC instead of cold water is you'll need to continue adding ice, or changing the ice/water mix during the process. The hot wort will quickly increase the temperature of the chilling medium if it's not replenished.
Personally, I'm having excellent results with my 40 plate (Rebel Brewer ChillHog 4000) chiller. I recirculate the wort through the chiller for the final ~5 minutes of the boil, sanitizing it (or sterilizing it). I then turn on the chill water feed and keep recirculating for about 5 minutes before I then direct the output from the chiller to the fermenter. I'm chilling ~6.5 gallons of boiling hot wort to the mid-50's to mid-60's (F) in maybe 10 minutes this way. I get the hot and cold break material (some gets left in the plate chiller, and the kettle bottom, but not that much) into the fermenter for the yeast to chew through. I use a hop spider to keep the hop matter out of the chiller, which really helps.
BTW, I started off my wort chilling experiences using first ice with extract (with specialty grains) along with cold water and setting the pot into a cold water/ice bath in the sink. That got old really fast. I then stepped to an IC, which was good for ~5 gallon batches, but easily took 15 minutes to chill close to pitching temp. I then went with the plate chiller, which before the pump addition took about the same amount of time. Adding the pump to the mix really helps a lot.
Also, IF you decide to pump your boiling hot wort through the inside of an IC or through a CFC or plate chiller, make damned sure it's able to handle more than 212F without issue. The normal head on the March pumps is rated safe to 250F.