Thank you.
I think it's about collecting evidence in the least invasive way possible. To me, the priority is limiting damage while still allowing law enforcement to function. One of the key privacy advantages of how LE access to phone companies or gmail or similar is implemented that it allows them to be granted access to just the data in question and little more.
What really becomes a problem is when the evidence in question is only available from one source and there's no way to do it that doesn't run the risk of what I'm going to term information bycatch. At that point there are really only two viable options - allow the collection with bycatch or disallow the collection due to bycatch.
The first is a significant privacy risk. That said, it's also not a new one. As long as people have kept records or written letters, a search has run the risk of exposing the private information of other unrelated people. Certainly, the same concern applies to tapping phone calls, and that's permitted by courts.
The second runs the risk of hobbling law enforcement entirely. Without perfect knowledge of what a given document, packet, phone call, etc. might contain, it's impossible to say that a search will or will not invade the privacy of another person in addition to the subject.
My understanding is that a warrant is for information or items because it's known and understood that information bycatch isn't always avoidable. This is considered unfortunate but unavoidable, as there cannot always be assumed to be other and better options.
I think this goes back to my earlier point about design. If a system isn't designed to contain any breach, then any breach - legal or otherwise - will be uncontained. I think this is less a constitutional problem than it is a technology one.