[This post is condensed and clarified for the purpose of focusing on the issue of Nephi and Laban.]
When Laman first approaches Laban to ask for the plates, Laban's reaction to the request is nonplussing. He declares that "thou art a robber, and I shall slay thee" (1 Nephi 3:13); Laman runs, empty-handed. Next, Nephi suggests buying the plates from Laban with their family's abandoned wealth. When they bring the wealth to Laban, he "saw [their] property, and that it was exceedingly great, he did lust after it, insomuch that he thrust [them] out, and sent his servants to slay [them], that he might obtain [their] property" (1 Nephi 3:25).
Laban first accuses Laman of being a robber. He then commits a type of robbery by stealing Lehi's goods and attempts to have the boys killed to avoid the legal ramifications of his theft.
The next time Laban enters the narrative (a few hours later) he's passed out drunk (1 Nephi 4:7). Later, Zoram would ask Nephi (who was disguised as Laban) concerning the "elders of the Jews", whom Laban was "out by night among" (1 Nephi 4:22). It makes sense to assume Laban was out celebrating his newfound, ill-gotten gains.
By falsely accusing Laman of being a robber, stealing from Lehi's sons, and attempting to kill them to cover up his crime, Laban broke or attempted to break at least 4 of the 10 Commandments (don't kill, bear false witness, murder, or covet). According to Deuteronomy 19:16-21, anyone who accuses someone falsely of a crime "[t]hen shall ye do unto him, as he had thought to have done unto his brother... thine eye shall not pity; but life shall go for life, eye for eye, tooth for tooth, hand for hand, foot for foot". Therefore, according to Mosaic law--which Laban would be obligated to live by, as a civic and possibly military leader--Laban should have received the results of what he tried to do to Lehi's sons. Laban was worthy of death, according to the law which he had agreed to live by.
Laban's appointment as a civic leader, God's command to Lehi to flee the Jews or be killed, and the account of Jeremiah's dealing with the Jewish leaders at the time all suggest the Jewish legal system was corrupt. There was probably no chance that Nephi could have received just recompense and protection from Laban by appealing to the priests and judges (probably the same 'elders' with whom Laban was carousing with that night). With the legal system corrupt and failing, the necessity for Lehi's sons to escape Jerusalem without being pursued to avoid being killed, and Laban being guilty of crimes punishable by death, it was expedient that Laban should die.
But, why have Nephi do the killing?
Regarding God's choice to have Nephi act as executioner (instead of a heart attack or lightning bolt), was God conditioning Nephi to respond to violence with more violence? Did God command Nephi to commit an immoral act of murder? Later accounts in 1st and 2nd Nephi show that retribution and violence are not in Nephi's nature, as his older brothers' repeated attempts on his life are continually met with forgiveness, patience, and love--not violence. Nephi already knew how to love and forgive his enemies. That wasn't what Nephi needed to learn.
Nephi, by his openness to God's love and showing that love to his brothers, had already received a promise from God that he would be a "ruler and teacher" in the future, so long as he continued to keep the commandments (1 Nephi 2:16-24). He was the first ruler of the righteous branch of Lehi's posterity, and was so beloved by his people that they called every king after him "Nephi". That position of leadership and authority would require him to teach his people, show near superhuman amounts of patience and love, and lead his people on the field of battle to protect themselves against their enemies. Nephi's position would require him to understand the full breadth of the human experience, including the gravity and consequences of taking a life.
Nephi was naturally a peacemaker, as evidenced by the fact that he recoiled at the Spirit's constraint to kill Laban. However, to be the kind of leader that the future Nephites would need, he needed to be able to make the hard choices when the time came. Cowardice or too much hesitation at a crucial moment could have meant the destruction of the Nephites. His experience in Jerusalem prepared him to be a righteous king in the future.
By having Nephi kill Laban, the Lord was expanding Nephi's pool of experience and knowledge of human nature. By giving him the grim experience of killing Laban, the Lord was showing Nephi the very dire consequences of continual rebellion against the principles of love and truth, and the difficulty faced by God Himself as He had to make His own hard choices. The entire lesson, as deep and poignant as it was, was summed up by the Spirit's words: "...the Lord slayeth the wicked to bring forth his righteous purposes. It is better that one man should perish than that a nation should dwindle and perish in unbelief." (1 Nephi 4:13)
