I should have the time to produce one for the September commitfest, but if you (or anyone else) want to work on this, I won't object.
My opinion at this very moment is that we should leave the the DEFAULT verbosity alone and add a new one (call it COMPACT or such) with the suppressed context for non-ERRORs.
Well, turns out there isn't really any way to preserve complete backwards compatibility if we want to do this change.
The attached patch (based on Pavel's patch) changes the default to be slightly more verbose (the CONTEXT lines which were previously omitted will be visible), but adds a new PGVerbosity called COMPACT which suppresses CONTEXT in non-error messages. Now DEFAULT will be more useful when debugging PL/PgSQL, and people who are annoyed by the new behaviour can use the COMPACT mode.