What I personally hope for is that people achieve a balance between safety and privacy.
Relinquishing privacy puts a society on a path where all power accrues to the state, to the detriment of all citizens.
States will prefer the former to the latter and firms will provide, at which point I don't think that the definition of safety-from is necessary.
I do believe that, at some point, people will as well. If other options prove too expensive or too inefficient, it's not just states that will prefer near complete mass surveillance.
Sure if everyone lives in a police state under the thumb of the government you're safer from petty crime but you're a heck of a lot less safe from government abuse.
I don't generally subscribe to conspiracy theories, but I do genuinely believe we're (in the US at least) being groomed for some sort of repressive state apparatus using this type of software to 'keep us safe' in the next decade or two.
Surely it's not difficult for you to imagine fairly common scenarios where your equation is patently untrue. A battered spouse of LEO or a non gender-conforming individual in a theocratic society are only two really easy examples that come to mind.
If we assume that individuals who control or have access to surveillance mechanisms are universally magnanimous and actually capable of neutralizing threats to safety, then your negative relationship between safety and privacy might hold up to scrutiny. I have more than a bit of trouble seeing how that assumption is anything other than utopian.
What leads you to think that this is always true? Do you not think there are any other solutions to reducing crime other than increasing surveillance?
Perhaps you would have more luck trying to build a foundation on the relationship of risk management and privacy. Mitigation vs acceptance vs avoidance, etc.