Amazon isn't providing these devices out of the kindness of their hearts. They are a for-profit enterprise, they do not care about making your life "easier" -- they want your money. They do not give a damn about anything else, and I do not believe that it's overly-paranoid to say that if you think otherwise then you're fooling yourself. It has been proven time and time again that if a thing can be abused by others for their own gain then they will be, almost without fail. Be it the government, a company, an individual, whatever.
Amazon has already done the hard work by getting the device into your home (which you paid them to do. and walked it into your own front door yourself). It's a marketers wet dream, and we all know -- or, at least we should know by now -- how sleazy marketing is. Do you really trust them to not use that always-on microphone? Do you actually trust that they are deleting any "non-relevant" data, or even keeping the 'relevant" data safe and out of the hands of others? I do not. You shouldn't either.
It has always baffled me the things people are willing to be duped out of under such a simple guise as "convenience". I've never been able to wrap my head around it. And I refuse to buy into the defeatist attitude of "privacy is an illusion" -- that's a load of crap.