"Serving the public" for a Christian takes many different forms, none of which is singled out by Jesus as something that every Christian is to participate in.
We know that Jesus never told Christians to go out and seek to govern other people, but that doesn't mean that He would not put an individual Christian in a government job for that person's livelihood and that person would then be in a position to witness to others.
But nowhere does Jesus even give the slightest hint that the purpose of a Christian is to get themselves installed in the government so that they can govern people.
That notion comes from the mind of man and cannot be supported by Scripture.
Uh, so Joseph didn’t end up in Pharoah’s household and ruling as Pharoah, thereby bringing about deliverance for the Jewish nation... or Esther didn’t affect public policy...and Paul didn’t try to convert Agrippa...
What about the importance of stewardship? Are not we, the citizens of the US (if you are a US citizen) called by God to steward what we’ve been entrusted with?... a country where men are not to dominate other men, where the poor and rich are equal in the eyes of the law, where God may be worshiped freely...etc, etc, etc.