In an imaginary world where an unconstitutional privacy infraction could be demonstrably proven to prevent a million deaths per year, the Constitution would be amended.

You're completely missing the point.

Let's take the worst-case disaster scenario: Terrorists are going to get a nuclear weapon and blow up a major city every year. Millions of deaths per year.

Here are two ways to prevent this:

A) We read everyone's private correspondence without prior suspicion and arrest anyone who we think has obtained nuclear materials necessary to make a bomb. Obviously if we hadn't arrested them they would have killed millions of people, so reading everyone's private correspondence without prior suspicion has saved millions of lives per year.

B) We track down and secure all the nuclear material (e.g. what the Russians have lost) using traditional investigative work so that terrorists can't get it. Since it's too hard for them to make themselves, this prevents them from obtaining a nuclear weapon, problem solved.

C) We send undercover operatives into terrorist networks and disrupt them before they ever get off the ground.

You don't need A if B works. You don't need A if C works. You don't need A if any of D through Z works either.

Non-renewable energy sources are being continuously depleted. Mankind's options are:

1) Conserve energy through efficiency.

2) Develop renewable energy technologies.

3) Invent cold fusion.

Sure, we might not need 1) or 2) if 3) works, but without the existence of 3), it's very easy to make a case for 1) and 2).

Except that in even the mid-long term (several hundred years) non-renewable energy is reasonable. (Based on estimates of Uranium and other fissile reserves)

And of course by the time that runs out, we'll have something like Planetary Resources up and running...

So while 3) might not ever happen, that does not imply 1) or 2) are the only remaining options. Proof by elimination only works if you can prove for all options, not just your preferred subset.