Yeah, being in the cart until you are able to walk safely with me and not dart away or tear the place up is a non-negotiable for me, so I never took them out to begin with so there was no battle. I still have to plunk my 4yo in the cart sometimes when she's particularly "energetic", and it's one time I have zero problem using a flat-out bribe: "I need you to ride in the cart because you're not being safe; I know you don't like to - I'll get you a pretzel to make it easier for both of us." I'm not usually a briber, but I seriously have NO patience for chasing a kid around a store, and at lesat I'm being honest about it, right? eep.
When they were under 3, my plan was always: bring a snack/drink, a couple soft books, and toys attached to the cart on strings/clips so they couldn't launch them, and just get it done as efficiently as I could. Give them their own list and pen sometimes, or a magnadoodle. Ask them to find things and point them out to you. Sing songs and dance crazy to the musak playing on the store speakers (I have no shame). They'd ask if they could get down, and I'd say no, 500 times if necessary. We'd try every once in a while at a smaller store where I only was getting 1 or 2 things to see if they were ready to walk with me yet, and if they weren't the next time we went grocery shopping I'd remind them they had to be in the cart because they hadn't shown me they were ready to walk safely with me yet, and we could try next time we were at the other (non-grocery) store.
I think initially it's going to be rough making him stay in the cart and he'll likely be mad and loud about it, but if you lay out the new expectation, the reason why, and give him plenty to do while he's sitting there he'll eventually get used to it. I agree with trying to find a cart in the parkig lot if posssible so his feet never hit the floor of the store. You jsut have to decide to keep him in and not wind up taking him out if he's too loud, unless you're taking him out of the store completely (which I've also done, abandoning my cart and letting an employee know on my way out the door, carrying a screeching child - good times!).
It's as much about safety to me as it is time spent shopping; I probably count on one hand the times I've seen a kid under 3 walking safely in a store next to a cart, without darting, weaving, grabbing stuff, or almost knocking into people. It's what toddlers do and is developmentally normal, but as one of my favorite sayings goes, "developmentally normal does not necessarily equal socially appropriate"
; skittering around is fine when your'e at a playground or at home, but in a store where everyone is trying to get something done it's just not cool IMO.
It usually gets better around 3, 3-1/2 years old; at least it did for my son anyway, my daughter is a little more high strung than my son so she still has her "cart moments".
I actually think a fair amount of this has to do with temperament, really - DS was pretty easygoing about stuff like this, DD, not so much. So she was louder and more persistent trying to change it, it took her longer to get used to it.