When y boil is done i normally have to add a touch over 2.5 gallons to hit my 5 gallon mark. To make things easier we will assume a perfect 50/50 split wort to added water. Tap water also hovers around 50ish degrees because of the under ground waterlines and how our geothermal earth works.
50% 100 degree wort added to 50% 50 degree water makes your total batch right at 75 degrees total, perfect for pitching your yeast. If you simplly added the 50 degree tap water to your 212 degree boil you would end up at like 130 some degrees... i think you can easily see that is way too hot! even if you let it cool to 140 your ended up with a overall temp of 95 degrees with in my understanding can cause alot of of flavors...
If that is not reason enough, just trust that the guys making money selling you and me our kits know more than you and me combined haha!
You can always read your yeast packet, figure out your volumes, get your tap water temps and figure out EXACTLY what you need to cool your wort to in order ot hit your target pitching temp...
(Wort temp * gallons of wort) + (Tap water temp * gallons of tap water)
---------------------------------------------------------------------
5 gallons total volume =
The over all temp of your batch once they are combined save for a few oddities in thermal transfer and crap that you can i don't really care about as 2 - 3 degrees shouldn't ruin anything really.
P.S. the line of dashes are just one big division signe, another way to read that formula would be below:
((Wort temp * gallons of wort) + (Tap water temp * gallons of tap water)) / 5 gallons total volume =