You're talking about legal authority, which is important. However, de facto, police have far more power than that. Remember the police who act without restriction or regard for legal limits, including physical, emotional, and legal abuse, arrests, fabricated charges ('resisting arrest', threatening an officer, etc.) etc.
> They can, with sufficient evidence, arrest you and conduct a search of your person to try to uncover it, but arrests are a big deal; they can't dragnet arrest.
Police do arrest people arbitrarily and without cause; it's not so rare. They don't need a dragnet, they only need to arrest you.
> I assume the productive article to write here is the one framed around informing people that they shouldn't cooperate with requests like these.
> They can, with sufficient evidence, arrest you and conduct a search of your person to try to uncover it, but arrests are a big deal; they can't dragnet arrest.
Police do arrest people arbitrarily and without cause; it's not so rare. They don't need a dragnet, they only need to arrest you.
> I assume the productive article to write here is the one framed around informing people that they shouldn't cooperate with requests like these.
That might not be good advice for everyone.