The constitution does not say who "originates popular initiative". It doesn't disqualify an MP or even the president! The constitution and indeed any law is precise. Whatever is not prohibited under the existing law cannot be ruled to be offend the law.
I'm begging to think that the US system of judiciary appoints is proper and right.
If the judiciary must make a political decision, they should undergo a political process! If you make political decisions, you should bear the political outcomes. You should not.hide behind your politically insular judicial office.