What you said is mostly true. My kids love asking our Echo Dot “how big is the sun” because it results in her (uhoh, it) listing all the dimensions from wikipedia, which are you can imagine are quite big. We’ve a Dot as it’s nice and cheap, and sitting next to a hifi for when we want to play music. It’s moderately useful (weather report, news summary, and calendar update from shouting “alexa, what’s the news” whilst I put the kettle on). Having some “smart home” stuff definitely makes it more worthwhile. The music playback requires Prime, or something.
The trigger words are limited, just “alexa”, “computer”, or something else. Amazon, maybe?
They say that its only sending when you activate the trigger word and the lights come on. Whether you trust Amazon or not is your choice. Obviously if the NSA/GCHQ/etc either coerce or backdoor an Echo then they have access to an always on device in your house. Then again, if they wanted to bug your house they’d probably do it the old fashioned way anyway…