I don't see it. There is always a case for privacy. But if people consider the presidency corrupt it would probably be a good idea to grant the judicial branch more power. Because secrecy doesn't protect you against a sufficiently corrupt government, it protects the government from you.
Also I rarely have seen any government system installed in such a way that some kind of lawful intercept mechanism would be required to circumvent their internal controls; they almost always are set up in standard boring enterprise way where an admin user can easily access anything, reset any credential, etc. I have seen systems where people forgot the admin credentials or lost access to the admins, but even in those systems there were easy backdoors with physical access.
There are some systems designed to protect keys and admin access from lower tier admins (for crypto fill, etc), but with those they are generally not archival, just transport security, and there are ways to downgrade or replace keys on request. The judiciary also doesn’t in practice have any real ability to do things to the executive without cooperation of parts of the executive; if we had some insane civil war type situation where a federal judge wanted to enforce an order against the executive, it would be basically impossible to do so without some support of the executive (or an external force, like a state national guard). This isn’t how it should be, but probably was like this within a decade of the constitution’s ratification and has gotten more so with time.
I guess it wouldn't necessarily be the judiciary. What I am getting at is that what enables you to run a conspiracy against the government also enables them to run a conspiracy against you. When journalists starts ending up dead, like in Malta or Slovakia, you want to be able to unravel any connection the murderers had to political figures and not end up with a bunch of dead ends consisting of encrypted communication and currency. How to actually solve that in a good way is up for debate though.
Privacy protects you from any entity wanting to use your personal life to discredit you. Secrecy doesn't protect you since a corrupt government will intimidate, discredit or kidnap you regardless of merit. What protects you is being able to uncover their slush funds and secret dealings.
The 4th Amendment to the US Constitution basically says there is no justification for such powers. The entire foundation of the the US Government is a warning against the centralization of power.
China operates like you describe and people that think like that should just move there. Perhaps we could create a program to swap citizens between countries so people can live with their ideological peers.
From what powers? The 4th amendment does not protect you from "reasonable" searches. A corrupt government wouldn't care about the constitution, like during Watergate. I am not a US citizen nor in the US (so the 4th amendment doesn't cover me) and I have already spent a fair amount of time in China. But thanks for offering.