This just isn't true, though. Hotword detection fails frequently for me with Siri, Google Home, and Alexa. I haven't tried the others. They all pick up unrelated sounds and record them as if the hotword was spoken when it definitely was not. Not even a similar sounding set of words.
There are absolutely privacy implications for technology that does automated scanning and recognition of its environment. They are buggy, as all programs are, and they are hackable, as all programs are.
Being both potentially buggy, potentially hackable, and constantly alert and running algorithms on their environment is absolutely a valid and real privacy concern.
(See also: smart speakers listening for a hotword.)
Another problem is that the risk of abuse is too great, even if the accuracy was flawless.
If the accuracy were flawless then there would be zero false positives, and the aforementioned issue wouldn't exist at all.
Oh, and it is hardly the only issue.
Computers aren't like humans. They have the ability to permanently and irreversibly forget certain information, and they always do exactly what they're programmed to. A local, on-device facial recognition programmed to immediately discard information on unrecognized faces has exactly zero privacy impact. (See also: smart speakers listening for a hotword.)