Maybe there are more stored inside the machine for easy refill
I would maybe guess so.
The front of the machine does look like a door, but it doesn't open.
And there is no way in this technologically advanced universe that the inside of that massive fridge is dedicated to refridgerating that tiny little box.
After all, actual fridges in the game are the same size as our actual fridges, and they refridgerate a much larger area.
Either way it doesn't explain the fact that once you've paid you get access to all of the bottles stored in the compartment.
The New Vegas vending machines don't seem too much better.

At the very least the nuka colas are compartmentalised, so you maybe don't get access to all of them when you pay. Although there aren't individual doors for each shelf.
Also, the same machine still looks to only hold about 5 bottles, and doesn't look like more roll over once one has been taken out.
I think they kind of over-designed vending machines, to try and make them look unique.
When in reality, currently existing vending machines are pretty much the best design for such an object.