Is there anything wrong with simply letting the water you add to top off your wort do the chilling to bring it to yeast pitching temperature?
No, there is nothing necessarily wrong about using topping off water to cool your wort. But there normally isn't enough topping off water to cool the wort to pitching temperature by itself without applying an additional cooling method (the math is below). One reason to cool quickly to ideal yeast-pitching temp is to allow the yeast to get a nice head start before bacteria can get a foothold. Wort is an excellent bacteria breeding medium.
Let's assume yeast-pitching temperature is 70°F (20°C) or less.
Example 1: If you do a partial boil and end up with 2.5 gallons (9.5 L) of wort at 210°F (99°C) and top off with 2.5 gallons (9.5 L) of water cooled in the refrigerator to 40°F (4.5°C), you will only cool your combined liquid volume to 125°F (52°C). Your wort is now lingering at ideal bacteria breeding temperature.
I have a friend who has probably made at least 100 partial-boil, extract recipe kits over a 15+ year homebrewing career. He dumps tap water ice cubes into his hot wort, and claims to have had very few infected batches. Even if you are not worried about topping off with plain-old tap water (frozen or liquid), ice alone is not enough to get you to yeast pitching temp. My friend simultaneously uses a cold water bath in his kitchen sink.
Example 2: If you assume only 2.0 gallons (8.4 L) of wort at 210°F (99°C) and top off with 25 lbs. (11.3 kg) of ice at 5°F (-15°C), that gets you to 5.0 gallons (19 L) of wort that is still too hot for ideal yeast pitching: 87°F (30.5°C).
So you could then wait out the last 17 degrees F (9.5 degrees C), or also do a cold water bath.
BTW, many experienced homebrewers recommend that you use non-chlorinated or de-chlorinated, yet sanitary, water for topping off (and your boil). Chlorine in water leads to one of the most common flaws of homebrewed beer -- medicinal or chloraseptic off-flavors. You could use bottled water or reverse osmosis water, install a charcoal filter, pre-boil and chill your tap water, or use a campden tablet, to avoid chlorine in the water.
I use two of the above methods. I purchase two gallons of purified water and put them in the freezer. I get them slushy and add them to my wort while it sits in a sink of cold water with two bags of ice added.
So far so good!
Alton Brown dumps his boiling wort onto a brick of ice! Clearly there is more than one way to skin this cat.
Topping off is perfectly legit, however I will note that my immersion chiller is probably my single favorite purchase amongst all my gear.
I like all the ideas above and I and going to be trying some of them. So far, I usually put my top off water in the fridge at least over night. I top off right away and that usually gets the temp pretty close to pitching temp, around 100-105. (I usually brew ales with a pitch temp of less than 90). I then have a utility sink (or a tub would work) filled with ice water that i set the wort bucket or pot in. Obviously you want to be careful that the water doesnt rise high enough to enter your wort.
I usually dont have to wait much more than 90 minutes at the very most!
so far, no complaints :)