Besides the obvious dangers of the carrier falling off--which I've seen happen TWICE!--did you know that it can damage the seat? Those "hooks" are what lock the carrier into the carseat base in your car. "Latching" the carseat onto the shopping cart can damage the mechanism, and this can cause the carrier to become unhooked from the base in an accident. Do you really want your baby to fly around the car?
*ETA* Several people have asked for alternatives to putting the cart on top, so I thought I would update with some that I've seen/used. 1) wearing the baby. I know it doesn't work for everyone, though. 2) putting the carrier in the big basket and arranging your groceries around it. You also have the top area and under the basket to use. 3) bringing along a "shopping buddy" (or older child if you have one) to push a second cart.
It ticks me off when I see that because it says right in the instructions when you buy those stupid things NOT to click them onto carts. Mine stays in the car becaues it's a CAR seat, and baby gets put in a stroller or, more likely, a carrier when we go somewhere. Between two kids, I dont think my seat left the car more than five times total once it was put in until the time it came out, and I dont anticipate adding much to that number with number three.
I never knew that placing a car seat on top of the cart was dangerous. I mean, I just figured that's what they were designed to do!!!
But then I started to figure out that it was a bad idea. Just google search baby car seat falls from cart and you will find story after story that will break your heart.
Injuries and death from falling from an elevated car seat are 100% preventable!!! If I were to take my chances and my baby was injured or killed, I would just die because I know better. It's not worth it!!
Hate when I see this in the store! We never did it with DS. I laid him in the basket (with a cover over the seat and a little blanket/pillow thing that a family friend made for us) or I carried him in the front carrier. Putting the carrier in the main basket is inconvenient because there's no room for groceries but putting the carrier on the child seat is not a good alternative. So dangerous and the injuries are preventable :(