We use square meters in Denmark.
The diameter of a CD/DVD is 120 mm, so you can fit 64 CD's per m² if you order them in a grid (more if you do not)
A CD is 1.2 mm think. The ceiling height in my apartment is ca 2.7m, so I could fit 14400 CD's per m². If a DVD can store 10 GByte, that is ca 144 TByte.
The average rent per square meter is about $20/month (more in Copenhagen, less outside the big cities).
I suspect I can not store 144TByte in the cloud for $20/month.
You might argue that I do have that many DVD's. But then I do have many small corners and shelves that is not much use for anything else. And it would be even more unlikely to be able to store say 14 TByte in the cloud for $2/month.
Google Archive storage is $0.0012/month (3x cheaper than Amazon Glacier, which surprised me). 144TB would be $173/month, so 9x cheaper to keep in your home.
I think your estimate of how many DVDs you can put in a given space is a bit optimistic: you're assuming no protection between discs and that a floor-to-ceiling tower is stable. If instead we imagine putting them in cases that double their thickness and putting collections of them in boxes that add 10% to the total height, though, it's 4x cheaper to keep them in your apartment. But if you use Blu-ray instead of DVD it's 20x cheaper!
The average rent per square meter is about $20/month (more in Copenhagen, less outside the big cities).
I suspect I can not store 144TByte in the cloud for $20/month.
You might argue that I do have that many DVD's. But then I do have many small corners and shelves that is not much use for anything else. And it would be even more unlikely to be able to store say 14 TByte in the cloud for $2/month.