MY RESPONSE FOLLOWS:
Let's keep our eye on the ball here. Kings in the OT did not--in the strictest sense--prefigure older men and shepherds in the NT. True there may be lessons that we can learn from David in connection with congregational shepherding, but can we really contend that his life actually serves as a [strict] pattern for Christian shepherds?
It is true that David was not removed as king when he committed adultery (and had a woman's innocent husband killed!). King Mannasseh also committed unthinkable atrocities, but was in time restored to his kingship (he was removed for a time). Does this mean that if a pope or shepherd is guilty of murder or adultery, he should not be removed from his office? Even if we use your line of reasoning, the least we could say is that a pope should be removed temporarily (in the way that Manasseh was removed for a time).
Moreover, Paul did not say that a "bishop" (EPISKOPOS) could be irreprehensible if he wanted to be. 1 Tim. 3:1 says: DEI OUN TON EPISKOPON ANEPILHMPTON EINAI. In other words--it is a binding obligation placed on all shepherds: they must be irreprehensible (cf. 1 Tim. 3:7). If such shepherds do not remain blameless, they are not fit to serve God's congregation.
Are we to believe that popes are held (by God) to a lesser standard than other shepherds are? According to 1 Cor. 5:9-13, those who unrepentantly practice sin should be excommunicated from God's congregation. Do these word not apply to the "Supreme Pontiff"? Surely you would admit that there have been some reprehensible popes down through the centuries. And yet these men were allowed to remain in office because they were popes? I simply do not get it. How can popes be held to a lower standard than other members of their flock?