The suspicion is something what I could do wholly without.
Just use whatever dragnet method you already have in place and phone it in. Subpoena google for all searches done in all cities and go round up the folks whose searches match the names of the victims.
I'm sure your going to get a fantastic conviction rate.
A society like that already existed: It was called East Germany and petty crime there was nearly non-existent. What crime there was was mostly corruption and went unpunished (who will watch the watchers).
Former East Germans seem to prefer the society they have right now.
Well you could argue then that they should be allowed to look at everything because if they do they could discover any number of crimes by looking at all communications.
Here's the thing. Lets' say hypothetically there is a crime committed at a high school. Are people generally ok with the police opening every single school locker to see who is a potential suspect for that one crime?
And what if while doing so they discover evidence of another crime? Is that ok and usable? If it is then we get to a point where it's conceivable that the police will then use any reason to say there is a crime to which they need to open school lockers knowing that they will almost certainly find evidence of some crime in one of them.
Yes, yes, and yes. Police can open any (or all) locker(s) they want for any purpose, though generally they ask for permission from the school administration first, and they can and do use any evidence discovered. Pick your favorite BS legal handwaving, I think it's usually "the lockers belong to the school, and by its good grace allows[/forces] the students to use them"
Did you think this one through? Law is a lagging indicator of what society thinks is acceptable. That works in both directions: sometimes things are legal that shouldn't be, but also things are illegal that should be. Beware a lopsided bias, or you get a ratchet to a totalitarian society.
So why does the intent of the investigator, to confirm versus discover, matter? If evidence is highly probative, and doesn't infringe on anyone's property rights, what's wrong with it? There's no right not to have the government find out you did something wrong...