If I recall correctly, DDG claims not to keep a record of your searches, so a subpoena would not provide anyone with much information.
I don't really see how their model is sustainable at scale.
Now, this makes me wonder: What could be an equivalent implementation for e-mails. An e-mail host that encourages immediate download, totally deletes e-mail contents, deletes logs of any sort, etc. when you delete messages?
You could also try Bitmessage or Retroshare, where e-mails are automatically encrypted, and P2P (no central server).
That would be POP3.
And we also need distributed search engines (https://en.wikipedia.org/wiki/Distributed_search_engine).
https://help.riseup.net/en/privacy-policy
Of course, you have to trust them to actually do that.