Hacker News Reader

Some cloud services already detect and delete pirate content since they do deduplication/hashing, i.e. https://www.wired.co.uk/article/dropbox-dmca-position

The article you linked describes preventing the creation of a shared link, not actually deleting content from people's Dropbox accounts.

(previously worked there, not speaking on their behalf or from private knowledge)

How do they avoid liability for erasing my only copy of something I licensed?

ToS. They can do whatever they want.