I think cooling the wort first is recommended for 3 reasons:
1) The faster you cool, the better cold break you'll get. This will help with the clarity in the final beer.
2) If you're using a glass carboy (which you aren't) a rapid temperature change could crack it
3) To prevent hot side aeration (HSA). I think there's a bit of a debate over HSA being a valid concern, but the basic idea is that you don't want to aerate the wort until it's cooled. Pouring it into a bucket will certainly aerate it.