It's illegal in many states to record a conversation without obtaining consent which is something this product does as a matter of course. This product shouldn't be legal to operate in those states, so you don't have to look very far before finding critical flaws in this approach.

That said, "identify on challenge" is something that Google might be more likely to adopt rather than "identify on call pickup". The latter being something they might spend more lobbyist dollars to oppose.

But what you've said is certainly (or should be) a real concern.