I don't know about Alexa specifically, but I've seen stories where the police requested Ring videos from a neighbor's house, including cameras inside the neighbor's house that they could not have known of without Amazon's assistance, that were not pointed outside, and even, if I remember correctly, one that was in the neighbor's business in a completely different location, where the justification pointedly identified the neighbor as not a suspect, but Amazon gave over this video anyways.
They were requesting it from Amazon, not from the neighbor. And it absolutely is wrong (weird is not a word I would use to describe police using their power unscrupulously) to take data that you know is irrelevant.
You did not specify any of this information in your comment. You just said that without Amazon's knowledge the police wouldn't have known that the cameras were there.
Well in fact yes they could have. By just asking the neighbors. And then summarily submitting a request to Amazon to get all relevant video all in one go.
We don't know all the details of the stories you refer to, so you have to provide all relevant information. For all we still know, you are just making assumptions.
I don't know the specifics of this case, but maybe the investigators just asked in case there was an accidental trigger, or a real trigger etc. Seems reasonable for the detective to attempt to turn over any stone they can to aid the investigation.
I think if an Alexa device were present in a home in which a person named Alexa lived, they would reconfigure the wake word. A more likely hypothetical would be one in which the murder was named was Alexa, and the surprised victim exclaimed, "Alexa, what are you doing here!?!"