I love the idea of making your kid your partner in shopping. If he has to fetch the eggs, or the bread, etc., he'll feel SO important, and he'll be focused.
And don't underestimate him intellectually! I knows the bread packaging you use; he can be taught to open the top of the egg carton and check to see that none are broken, and probably even to carry it. If that worried you, then he can be the one to pick the carton and point it out to you.
You may have to spend a lot of time on teaching him, but BOY does he want to learn, and BOY does he want to be a grownup. Even if he's just *finding* the eggs, and looking for the one w/ the word "large" (he can recognize it if he can't read it).
Kids have AMAZING memories; grownups underestimate them all the time. Their brains are far more developed than their bodies.
I absolutely don't think you need to leave your kid at home or keep him in the cart. But you *do* have to invest your time and energy in involving him in the process of life. You need to plan on spending more time at the store--you can't zip in and out as if he's a package. He's a companion, and you'll have a better time (and a smarter and more compliant kid) if you treat him like one, and give him a chance to fully participate in your joint shopping trip, instead of just "coming along for the ride."
It would be a lot of fun, actually. The "Stop Your Feet" game was a TON of fun, and my kids really never did get that I invented it solely so I didn't have to worry about them running into traffic or getting too far away from me.
And I agree w/Hmmmm--yelling shouldn't be required (I'm not sure what you mean by "yelling"--you could simply mean "speaking a little bit more sharply and a tiny bit louder in a manner that is designed to catch attention"--it's a very flexible word).