(Interestingly, Jewish midrash on Joab is much more favorable than Christian commentary. Compared to them, the "critical" position discussed at the end simply assumes a flat-footedly unironic reading of the history).
Quick version: Joab is Zhuge Liang, David is Liu Bei, and the killing of Abner is like the occupation of Sichuan and the seizing of Liu Zhang's land.
In Three Kingdoms, the turning point comes when the brilliant, single-minded advisor Zhuge Liang insists that his leader Liu Bei follow the entreaties of the local officials and by betraying his host and kinsman, Liu Zhang, seize Sichuan as a base. Liu Bei's acquiescence marks the end of Liu Bei's political innocence and his realization that full integrity is in reality incompatible with founding a new regime. David's acquiescence in Joab's murder of Abner has the same significance. And in both cases, the ruler's tears of regret, however sincere, are secondary to his acceptance of the fruits of the betrayal.
The idea that Abner's survival would have been compatible with David ruling in actuality is simply absurd; having disposed of Ishbosheth, Abner would have soon disposed of David the same way. And of course the fact that Abner humiliating Ishbosheth by taking one of Saul's concubines is the very same thing that Solomon executed his half-brother Adonijah for merely proposing only confirms it. Joab's betrayal by David (who slyly waited to have his son Solomon do deed) is only the mirror image of the betrayals Joab had to commit to build David's kingdom.
What is the archetypal image of David's rise and rule, almost from the beginning? It is him mourning over the immensely convenient death of every rival, and so winning over the rival's people. The pattern starts with Nabal and Abigail, continues with David mourning the death of Saul and Jonathan that brought him to power in Judah, continues with him mourning the death of Abner, and Absalom, and Amasa. While it was the Philistines who do the job on Saul and Jonathan, and Joab who was the man stuck with the job of whacking Abner, Uriah, Absalom, and Amasa, God Himself was the hatchet man in the first archetypal case, that of Nabal. Regardless of the mechanics, Joab is a man who has identified himself with God's purpose as He founds the Davidic dynasty: that while David will keep his hands clean, all those who stand between him and the throne are doomed. (Not to speak of that opponent's wife and people being made over to David.)
Another facet is Joab's position (along with the priest Abiathar) as the leader of the old Israelites, as opposed to the purely royal and heavily non-Israelite establishment coalesced around the David's royal establishment, with his Cherethite and Pelethite guards, the mysterious Jerusalem priest Zadok, and Bathsheba, the former wife of the Hittite Uriah and her son Solomon. It is thus no accident that it is Joab alone, not Nathan or any other prophet, who speaks against David's plan to conduct a census and hence to tax Israelite and non-Israelite together without any reference to the old tabernacle tax. (The coronation of Solomon was the nightmare come true for the palaeo-conservatives of ancient Israel -- an alliance of immigrants, alien mercenaries, new-fangled big-city religion, and royal taxation agents.)
So who was right? Joab or Benaiah, Adonijah or Solomon? Abiathar or Zadok? Well, I prefer what the reactionary Ariq-Böke said when his defiance of his progressive brother Qubilai Qa'an reached its bankruptcy:
When he arrived at the Court of the Qa'an orders were given for a large body of troops to be stationed there, and the Qa'an ordered him [i.e. Ariq Böke] to make his submission. Now it is their custom in such cases to cast the door of the tent over the shoulders of the evil-doer. He made submission covered in this manner and after a while was given permission and entered. He took his stand among the bitikchis [scribes]. The Qa'an looked at him for a time and was moved with brotherly feeling and sorrow. Ariq Böke wept and tears came to [his brother] the Qa'an's eyes also. He wiped them and asked: "Dear brother, in this strife and contention were we in the right or you?" Ariq-Böke answered: "We were then and you are today" (Successors of Genghis Khan, p. 261).
The dynasty must be founded, and Joab has do wield the hatchet necessary to found it, so that the founder David may have clean hands. And the dynasty once founded must evolve beyond the narrow rural provincialism, and the hoar head of Joab and his militiamen must go down in blood before the Jerusalem temple-state. He was right then and Solomon is right now. And Jeremiah, descendant of the rejected priest Abiathar, who wrote the book, weeps for him and for Judah.
But it will not surprise anyone familiar with the political style preferred by those Protestant pastors who like to talk politics that their commentaries are always written in a pile-on delight in partisanship, and never in tears.
I doubt any one will read this, but it helped clarify my thoughts. The fact that Joab's story, utterly absorbing in the Bible, is unknown, is a testimony that the Deuteronomistic History, Jeremiah's story of the rise and fall of a kingdom, is today read as anything but that of the rise and fall of a kingdom.