I have an Echo and it is helping Amazon get better at selling me stuff. When I try to list the probable or even possible harms from this, I can't come up with a lot.
Compare that to something like driving my car. 100 people every day are killed in their car. Even so, I still drive because the expected utility of getting to point B is much greater than the expected harm from doing so.
I use a car and the worst case scenario is death or permanent disability, right? People die in their cars every day.
So what's the worst case scenario for using an Echo? How many people a day does that happen to?
What's the worst case scenario from having an Echo? How many people does it affect each year? What's the dollar cost of that damage?
IMO, it isn't an imminent threat. It's not going to kill you. It's not going to cause you any physical harm. It's the slow erosion of privacy which is a detriment to everyone.
I'm going to avoid the cliche Orwellian arguments and the normalizing surveillance arguments. Both of these have been addressed ad nauseaum. I'm going to go a different route and see if it resonates with you at all.
It is incredibly easy for humans to be manipulated. This only gets easier as we have treasure troves of data about individuals. Amazon has many of the smartest people in the world working to manipulate you to do things in their best interest. Sometimes their interests lineup with your best interests and things are great. Other times, their interests will be negative to your life.
It is in their best interest for you to not be content with what you have. It probably is your best interest to be content with what you have. It's not wrong to want things, but things will never fulfill you.
I'm not saying capitalism is evil, Amazon is bad, or that we aren't living in one of the best times in human history. I am saying that putting a marketing device (which is also a privacy concern) in my home is not something I am interested in. Especially when I can do the 90% with my phone in 5 thumb presses.
I like the driving analogy because even though the worst case scenario is about as bad as it gets, it's not all that likely. I think people, even here, have a hard time separating possibility and probability.
A connected speaker has real and immediate benefits for some people. People that use it to buy stuff (I do all the time) aren't going to see ads for associated products like website shoppers do. Frankly, if the Echo scares you, https://amazon.com should scare you even more. I bet they collect a lot more data in a 10 minute browsing session than they do with months of Echo use.