I would argue that it's a difference in quantity which produces a difference in kind. When the "papers" in question contain e.g. a complete history of your location for the last four years, along with all of your communications to everyone you know, any search of those papers is by definition open-ended.
The same principle already applies both in the UK and USA to physical searches of your person. If you're being searched for a weapon then patting down is a sufficient search, a strip search is not.
I don't think that's true. Anyone who kept a personal diary back in 1776 probably recorded more information about their activities and thoughts than an ordinary smartphone user today. And the detailed letters many people wrote each other back then probably reveal a lot more in the way of private thoughts than peoples' text messages today.
Undoubtedly the average person records more today than the average person in 1789. But that does not mean that more detailed record-keeping would have been beyond what people back then could have anticipated. Given the phenomenally detailed records we have from some people at that time, I think it was well within the contemplation of the framers that getting a warrant for someone's desk drawer could reveal extensive personal information.
Not to volleyball this, but I don't think that's true. Any information in a personal diary is there because it was intentionally, explicitly entered there (even if with the expectation that it would remain private). There is a lot of information on most people's phones that they have not intentionally, explicitly put there.
Remember the question we are discussing: could people in 1789 have anticipated the kind of invasions of privacy searches of smartphones enable today? Given the kind of detailed records some people back then kept, not just bland metadata but detailed accountings of their thoughts, I think the answer is "yes."
We are still a long way from smartphones automatically capturing the kind of private thoughts people choose to write down (back then as now).