If you completely remodeled a kitchen around a chest fridge it might not be too terribly inconvenient. But the major blocker is that virtually every kitchen is designed with a perfect spot for a tall, relatively shallow fridge.
Indeed. I could imagine a very neat one built into the cabinetry where the counter top could be lifted up or something.
It's inconvenient as soon as you need to get something from the bottom of the fridge, kitchen layout does not change this one at all. And I grew up in a home with multiple chest fridges in addition to a shelved ones so I know the hurdles.
They are good to store something you're not accessing all the time though, like frozen berries etc.