With a deep fridge you can push things to the side, reach over them, etc... you can still kind of see where everything is if you move your head to look around other items.
With a chest fridge you stack everything.
This can:
* more completely obscure other items
* squish items
* require you to move items to find what you want (i.e. pile them on top of other items)
Then you have things like... cartons of milk and various other bottles, which aren't designed to be stacked vertically, but are mostly optimized to be next to other items.
You also lose the utility of having a smaller shelved door area. You can have a level of shelving in a chest refrigerator (basically sliding racks/baskets)... but these become more things you need to move to see other things. With doors they're naturally out of the way on fridge open.
You also have the problem of spills. In a standard fridge a spill means I pick up items, wipe the bottom, put them on another shelf temporarily... then wipe the shelf and replace. Needless to say, spilling anything into a chest refrigerator is a nightmare. You have to remove nearly everything... and since so much is stacked, it's much messier.
A deep vertical refrigerator already completely obscures most of its contents, requires you to move items in order to get what you want, and contains drawers where the contents are not only stacked but completely invisible until you specifically open the drawer to search inside.
Your reference to moving items in the fridge from one shelf to another shelf (temporarily) in order to clean up a spill tells me that you're not engaging in typical deep refrigerator use. The other shelf is already full; to clean up a spill, you need to pull the things that were in the dirty area out of the fridge.
But why not have a chest freezer underneath the countertop, but as a pull-out drawer? Same benefits of a top opening, but no need to dedicate a section of countertop for the lid to open.
But yeah, for a fridge, that’s not as easy.