That's wrong for many reasons. Others have covered the simple fact that you couldn't start any app with lots of users and zero capital. The downside is huge. Barriers to entry become more impossible than they already are.
But that's not the worst of it. The Economist here is doing a static analysis, oddly enough. They're making the simple observation that if things cost more or have more risk, they get more attention.
That's if they have more risk today. Once you collect data, it doesn't go anywhere. Every bit that sits on your servers can easily be copied to another server, today, tomorrow, ten years from now. Do you know what all the bits are on your computers?
This isn't copyrighted DRM or porn. You could have a blob hashes and userids. If I put that on your computer, would you know? Could you be expected to find it? Know what it was?
As Facebook and the other platforms are demonstrating, this data continues to have value many years after it was collected. And once somebody gives some data to you, it's effectively both invisible and trackless. Over long periods of time, your cost becomes infinity to maintain this risk. Meanwhile, attack vectors get better and people come and go out of your offices all the time. Could you manage that risk? Forever?
I can't think of _any_ sensitive data on the web that's stayed safe. Why would attaching any amount of value change that?