The way the system is intended to work is that such things should be enacted through the legislature or a Constitutional convention. If it is universally desired to elevate something above reproach (and shoddy prevention that is given the treatment of the 1st, 2nd, 4th, 5th and 10th Amendments in general), it'd make it into the Federal Constitution to clarify it. Interestingly however, the 10th Amendment explicitly makes implicit that any freedom not explicitly carved out in either a State or Federal Constitution is granted to the People. So somewhere along the way we've seriously lost sight of how things were intended to work.
The American Constitution was intended to primarily enumerate limits on Government, not on those of the People. Therefore, positive assertions or explicit "People have X right" is actually in a sense a form of regression from what the document was intended to embody. Which again, is primarily "no government, no matter how much easier it'd make your existence, thou shalt not go there", and "no States, we all talked about this, you shan't go there either".
Oh we have that here as well, though I'm not sure about "conservative". Where I live, the supreme federal court is the legislative power. People vote representatives to propose laws but the judges of the supreme court are the ones who ultimately define what the law means in practice it and they use that power to legislate in what has been termed "judicial activism".
I've seen cases where the judges openly acknowledged in writing that according to the law the defendant was innocent, then proceeded to condemn them anyway because what they did offended their personal morals and therefore "deserved repression".