There is nothing impossible about it. We barely scratched the surface of data storage mechanisms. All it takes is another few breakthroughs and we likely can store all of Youtube of all times in a block the size of an ice cube.
1: https://news.ycombinator.com/item?id=23393293
2: I think I heard this use case predicted on some NPR thing I can't find, but this one https://www.npr.org/2013/01/24/170082404/shall-i-encode-thee... says “Agilent waived the cost of DNA synthesis for this project, but the researchers estimate it would normally cost about $12,400 per megabyte.
"It's an unthinkably large amount of money ... at the moment," Goldman says.”
I believe the first hard drive cost about $100K/MB in today's money.
Wouldn't want your only ice cube to melt