I'm not too sure Siri/ Google Assistant doesn't do this already, but to serve us ads.
Currently, ML models are too resource intensive ($$) for always on-recording.
As far I as understand, Siri works with a very simple "hey siri" detector that then fires up a more advanced system that verifies "is this the phone owner asking the question" before even trying to answer.
I'm confident privacy-sensitive engineers would notice and flag any misuse;
If it did, traffic analysis would probably have revealed it.