One reason to do the fridge/decant method is when you are pitching a lot of starter into a beer and you don't want to affect the taste, color, and/or gravity of your wort with the starter beer. The reason for putting it in the fridge is to get the yeast to drop as quickly as possible.
This method is also what you'd do if you were going to do a multi-step starter where you would decant off the starter beer and replace it with fresh starter wort. The length of time you keep it in the fridge depends upon how long it takes to cool it and for the yeast to drop, which is strain dependent. Since I'm not worried about trying to cut the time to a minimum, when I do it I would prepare my starter the weekend before and let it sit in the fridge until about Thursday.
By the way, I do my starter the same way as you, except I will give it a little more time to ferment. If I'm brewing Saturday, I'll usually get my single-step starter going Thursday night.