I suspect most of us share paranoia about these things and don't own them. But if you do own one, it might be time to reconsider.
In an email sent to customers today, Amazon said that Echo users will no longer be able to set their devices to process Alexa requests locally and, therefore, avoid sending voice recordings to Amazon’s cloud. Amazon apparently sent the email to users with “Do Not Send Voice Recordings” enabled on their Echo. Starting on March 28, recordings of everything command spoken to the Alexa living in Echo speakers and smart displays will automatically be sent to Amazon and processed in the cloud.
It doesn't sound like they're bothering with doing something like Apple's differential privacy.