I've been doing that all along and it's not hard. It's actually easier than 6 in, 2 out, 3 in, 1 out, 5 in, etc. You just make them take it out of the cart and leave it behind. Say it's a safety issue, fire and OSHA regulation, in case an emergency requires a quick exit and the shopping cart would be an impediment. Remembering the guest in room 3 has 24 items is no different than remembering the guest in room 3 has 4 items. Just do a careful count in and out. Most people carry things in a way that make it pretty easy to count or will happily put in on the bar for a count, the ones that have them balled up or draped over their arm I offer to help carry and count as I'm taking items from them. Count out, same thing, they usually have the "yes" in one hand, the "no" in the other, and taking a few extra seconds in taking the "no" from them allows for a count out.
I knew that corporate policy is no limit, but I was also told that I could limit to what I thought I could handle. Then early on in me being at Spot, I tried to limit a guest who had 20 items to 10 at a time. She said "You could count in 10, then count out 10, then 10 in again and 10 out again and I would have to get fully dressed again halfway through. Or you could count 20 in and 20 out and I don't have the inconvenience of getting dressed and then undressed." She was right, 20 in and out was just as easy as 10 in and out. Since then, guests love not having to figure out what to take in first and not having to get dressed to try on additional stuff that they had to leave outside the room.