Do you have any specific examples of debug parsing in mind? The things I'm most familiar with is parsing logs, which should be a benefit, not a problem to solve. You can't really violate privacy by parsing debug strings, since you won't be able to create the types anyway.
A much bigger privacy violation is using transmute and offset_of! (which you seem to not consider an issue). That thing cannot be disabled in any way, and allows to directly read (and write) private memory of any type.
That's true, but Debug is not the only thing which affects the panic formatting. It seems more reasonable to have an option for shorter or no formatting messages in panics, for the sake of small binaries. Or even remove unwinding entirely, and use panic=immedaite-abort. That should solve the Debug issue as well.