I know multiple people who use voice assistants like Alexa that are effectively wiretapping their house. When asked how they feel comfortable with that, they say, "Well, my phone's already compromised anyway..."
I think people do care about privacy, but right now they just don't see any practical way to make it happen. The root of it all is the smartphone itself, because "Don't use a smartphone" is not a serious option.
It's all about the risk profile you're willing to accept. I personally have much more private information accessible through my phone, computer, and certain cloud accounts than I do from things I'm saying in my home, and I believe a malicious actor (potentially including a large corporation like Amazon or Google) would have a much easier time and/or would be much more likely to engage in tapping one of those sources than a voice assistant in my home.
It's certainly very possible - there was a recent story about how a malicious Alexa skill, if downloaded and installed, could siphon your entire voice history - but those sorts of risks also exist for almost any internet-connected device you own.
So, in my opinion and going by my own risk profile, those people responding "my phone's already compromised" are behaving rationally.
I put the statement "my phone's already compromised" in the same category as "I don't have anything to hide". Those may very well be common natural behaviors, but I wouldn't call them rational exactly.
True. Wire tapping implies it only listens to you during an active "call" to Alexa. Alexa is more like a bugging device.