Not necessarily. Just because the compiler can't prove that g only returns true iff f also returned true doesn't mean the programmer doesn't know it to actually be true.

So changing that behavior means that the compiler now rejects 40 years worth of correctly working legacy code (and some buggy code, as well). Newer languages (e.g. Java, C#) that don't have to support existing code can afford to do what you want and reject programs where a simple heuristic isn't enough to tell whether a variable is initialized or not.

You can already break a lot of programs with -Wall -Werror (I generally compile my code with both, but turn them off for libraries). Just hide the amazing optimisation behind an -foptimise-undefined-behaviour which you can only turn on if you've specified at least a significant portion of -Wall.

So don't raise an error, instead publish a warning.