As a shopper I never go in anticipating I will be purchasing merchandise that will break, fail or fall apart, no one does. But it happens every day.
So some people have learned to keep receipts until these are no longer needed. I happen to keep mine in a drawer in my desk. I go through these every couple of months and toss the ones that the return date has passed.

Each store has its own policy, most times listed right on the back of the receipt. And not meaning to be sarcastic, there are signs posted that all customers probably are reading while standing in line that read the return/echange policy. But we never think it pertains to us and we go up and want our merchandise exchanged.

I agree that the exchange could have taken place...but then Target has one of the more restrictive policies out there.
And while the coat you bought at Kohl's may last a bit longer before she outgrows it they still request a receipt to return or exchange.