I was more thinking along the lines of immunity from National Security Letters[1], which could be marketed to companies or individuals who want an extra layer of privacy guarantee.
For example, here is a quote from Dropbox's 2016 Transparency report[2]:
"We believe that those who use online services have a right to know if the government requests their data, and that service providers have a right to notify them of these requests. Often, though, requests for user data are accompanied by court orders preventing Dropbox from providing notice."
An EU-based Dropbox clone could market this as a unique selling point, that the above doesn't apply. Swiss banking for your online storage, if you will.