So we're clear, you believe there should be a law that, when a police department collects information about you during a criminal investigation, they should notify you directly that they've done so?
It does make sense. Police are absolutely not beyond reproach, and there's screwups all the time. They need to be held to a high standard.
It's also easy to imagine reasonable compromises, like a time delay where they only have to report after e.g. 48 hours, and allowing a system whereby a judge can issue a warrant to extend that delay.
That's more or less what a search warrant is, so yes.
Yes.
Specifically, I believe that if information that is held by a private 3rd party I accessed by anyone, law enforcement or otherwise, that third party should be required to tell you that it was requested and by whom. Just like they can't put a gag order on a search warrant to your home, this hypothetical search would be exempt from gag orders.