Let's be fair, the product is designed to specifically not do that:
"Echo uses on-device keyword spotting to detect the wake word. When Echo detects the wake word, it lights up and streams audio to the cloud, where we leverage the Alexa Voice Service to recognize and respond to your request."
Of course, given that a lot of the HN crowd currently derives their income from surveillance and/or walled-garden based business models ("analytics", "big data", "software as a service", etc), I expect to be down-voted for suggesting that it is a bad idea to trade your future for a few shiny (and sometimes useful) toys.
I hope everybody that uses Amazon's microphone - or, as you say, a cell phone - realize that you're creating the surveillance state. Right now there is a large effort to normalize surveillance socially, and instead of fighting for you right to privacy, we have a threat full of people talking about how wonderful the bait tastes.
We need AGPL algorithms and training datasets for voice recognition, plus user-programmable open-source firmware for on-device wake word recognition.
If we can end the false privacy-convenience tradeoff, then the technology can be applied for goals defined by users rather than select business interests.