Sounds like a good idea in theory, in practice though, nowadays very few people have a house with a basement like that anymore, unfortunately. I don't get it myself to be honest, it's more efficient use of the ground surface area a house occupies.
I'd go with a chest freezer in the basement and a small fridge in the kitchen for frequently used / quick access stuff (milk, tonight's dinner ingredients).
I meant the opposite. I do indeed have a (very) unfinished basement that gets a bit wet with a freezer. Many people won't want a freezer in their downstairs living room. At least that's how I took the comment.
My basement is 80% finished, but the freezer lives in the unfinished part. But "unfinished" is relative, I still have concrete floors and walls with insulation on the walls, just no sheetrock and bare rafters on the ceiling.
Yeah, you don't really want to run down to the basement every time you want some ice cubes or cream for your coffee.
But that's more or less what I do. I have a (not small) fridge in the kitchen and an upright freezer in the basement. (I find chest freezers can become something of a black hole.)
When I had a 48-hour power outage recently, the freezer upstairs was pretty much defrosted--which was mostly fine because I didn't have perishable meat/fish up there. But the freezer downstairs was fine. (Made a point of keeping it buttoned up the whole time.)
I'd go with a chest freezer in the basement and a small fridge in the kitchen for frequently used / quick access stuff (milk, tonight's dinner ingredients).