Given the power demands of such an always-on analysis engine, that would show in battery runtime. At least if it's happening while the device is not plugged in.
On iOS, the word "Siri" can be detected at any time (if set so).
Maybe (just an hypothesis) there could be a set of other keywords also listened for, that once detected could start another more complex routine. Like that, you could limit the battery impact, and yet be able to listen to the users for advertising purpose.
On my Motorola from 8 years ago, the voice command was "OK, Google" or any custom short phrase you trained for it. But I think it would be really hard to get a useful but concise list of keywords... It would certainly be possible to listen for, say, "new Subaru" and show an ad if that one thing was detected, but the point is that you want to select which one of a million ads to show you'd need far more keywords, which gets computationally expensive quickly. It would probably be more battery efficient to compress audio that sounds like speech aggressively and then send it up to The Cloud for analysis...scary stuff, and part of the reason I don't have any home assistants!
A lot of people anecdotally believe this "they're listening", but I don't, since if it happens offline, it would consume a lot of power of the smart devices, and if it happens on the cloud, then the bandwidth and computing requirements would be gigantic and probably have poor ROI that it's not worth it. But maybe I'm overestimating those requirements.
Then again, I opened Instagram at a carwash once, and a few days later I got ads about car treatment products. I walked by an e-bike store the other day and stopped for about 15 seconds to look at the bikes being displayed, and a few days later Instagram started showing me ads for the brand. I thought Instagram or another Zuck-app was tracking my location, but I just checked and none of the Zuck-apps on my phone have location permission enabled.
Maybe (just an hypothesis) there could be a set of other keywords also listened for, that once detected could start another more complex routine. Like that, you could limit the battery impact, and yet be able to listen to the users for advertising purpose.