Might be monetarily cheaper but then you have Amazon listening in on your whole house so you have the cost of trusting them with your privacy.
... you don't think Apple is listening, despite being busted last year for doing just that?
First they said Siri doesn't record ANYTHING, then they said Siri only records ACTIVE requests for quality assurance, then they said their iOS API's prevented other apps from listening in without notifying you. Well they lied, they lied again after getting caught lying the first time, and last week I was presented with ads for rotary sushi restaurants on four separate apps that were not running at that time an hour after mentioning it in a phone conversation. I HATE sushi, I haven't discussed, searched for or even thought about sushi let alone restaurants that serve it rotary style in years, which is how that topic came up in conversation as I was discussing how a place that used to be popular in high school was shutting down because of dropping sales blamed on the Rona. But please, Apple, tell me again how Siri and iOS protect my "privacy."
Alexa devices have a hard button on the top to mute their mics completely. I don't see that functionality anywhere on the HomePod line, hardware or software based. If you're placing a a smart speaker in your home, you need to accept that your conversations are going to be recorded and used for marketing purposes etc. If you cannot abide this, don't get a smart speaker, but at least don't kid yourself into thinking Apple is any different than Amazon in regards to this issue because they've already lied a couple times about it.
https://www.cnbc.com/2019/08/28/apple-apologizes-for-listening-to-siri-conversations.html