Have you tried this lately - in the last 10 years? things used to be bad, but clang and gcc at least have really cleaned up their act, most warning are now zero false positives and so you want to clean everything up. The only time I see the issue you described was when someone upgraded the compiler, and the new warnings were all real bugs.
Static analysis tools are a different problem: I find that most of them have so many false positives they are not worth looking at.