It is possible to be morally admirable but not terribly effective. Whether fairly or not, Jimmy Carter is widely viewed as the best recent example of this combination. Some would place Woodrow Wilson in this category. Every so often we are blessed with both effectiveness and integrity. Further, there is both a link and a distinction between private and public morality.
Character is revealed in every action.
The distinction is that an officeholder is primarily responsible to the public for conducting the public business of that office responsibly. That public business consists of the evaluation, promotion, and implementation of public policies that affect the common good. Hypocrisy, religious sham, and the abuse of religious language and symbols are probably inevitable, given American religiosity. I shared the view of many at the time that President Clinton's use of the language of repentance and forgiveness during the impeachment crisis was at best dubious. While no one can get inside another person's soul, one can examine public acts for the fruit of repentance.