I think you can achive that way easier, than with a box for every item. You could Show an example item, and when you pay for it, it could be prepared for you with all the other items at the Exit.
But I don't think, this is really a good use of BTC. Do you really want to pay for every item individually? Sounds like a lot of work even if it just scanning and pressing "send".

When I think, about it, there could be this box at the Exit, which can be unlocked by paying for it.

We have those now, it's called a vending machine

What you described could be achieved by having rows and rows of vending machines in a supermarket, and it won't be a supermarket anymore. Besides, I do not want to shop there.

In the UK alot of stores come with a hand scanner, so you can scan the item as you put it in your trolley and pay at the end. Sometimes they check to make sure you have scanned the correct stuff. Its nice and easy, and lets you pack as you go.

http://www.tesco.com/scan-as-you-shop/

ahahah I imagined a full automated vending machine but a HUGE one!

Walk up to it and choose one by one

But you'll have queues while people wait for their milk, then their bread, then what if they dont want that bread now?

Ok thanks guys for the input. I see the limitations of this idea. Maybe it could work with small, more expensive items with not much demand (expensive hardware, jewellery).
Where I live we do have shops with checkout counters with scanners. This is probably faster than the bitcoin boxes i proposed, but the automatic counters always have personnel standing nearby helping newbies and checking for fraud, rendering the idea a bit pointless.

This isn't really a bitcoin thing; one could obviously have such a machine and it could accept anything as payment, bitcoin, credit card, etc.  They already have these all over the place here, it would simply be a matter of adding bitcoin as a payment option.
Personally, I hate them.  The convenience store by me has nothing but these and they NEVER work.  They have four of them, and I have never been in the store when more then one was working correctly so there is always a huge line.  Plus there is always some dumbass who doesn't  know how to work it and holds up the whole line even more. 

Fully automated? Do you have any idea the cost and infrastructure required to implement this idea? If this was easy and cheap, then we'd be seeing all these automated machines replace all the employees in groceries and other B&M stores by now.

so you propose to have plastic security boxes per item.

well:
1: the deli counter will have lots of boxes with meat oozing into the boxes, meaning they have to be washed
2: same for the veg section many boxes. meaning that would have to have a box per banana, potato, tomato
3: the freezer section. plastic, electronics dont work well on ice

now lets get into more detail
1: a raspberry Pi per box costs more in maintenance and purchase to fill a store of boxes. then 3 peoples salaries
2: refilling each box and locking it takes more time then just dumping stock on a shelf, costing more salary in labour of shelf fillers then th couple of cashiers they would save
3: if there is no one at the cash desk/exit as it is presumed all stock is paid for then great. ill have this 50c banana oh and i get a free raspberry PI and a secure box to take home with me as there is no one to stop me
4: instead of just picking up a can of baked beans. i have to scan a qr code, open the box, take the tin of beans out and then put it into the trolley. 1 second food choice turns into a 20 second chore.. wait... also the 10minute confirm time before it unlocks
5: i then have to dump the emty box somewhere (unless point 3. i take it with me )
6: i am now at the exit and have to start bagging up my stuff in view of a security guard to make sure i dont do point 3.
7: staff then dont only have to take stacks of baskets away from the cashier desk, but a whole stack of security boxes too.


honestly id rather take my items that were never security boxed to a cashiers desk and pay in one go. an idea such as the OP proposes would work for parking meters, newspaper vending machines but individual payments in a multi-product scenario is not time efficient nor is it cheaper. (imagine the 20 items in your trolley. that's 20 TX fee's if your hoping to get to your car on time)

seems the OP has not worked in retail or hasnt put his idea into a 'working scenario' (feasibility study)

what would work is a food vending machine. where instead of typing in E7 for a bottle of pepsi. you scan the QR code that represents E7 and the vending machine monitors the 30 qr codes (1 per product type) and spins the coil to make the product fall into the collection bin at the bottom, when it receives a payment