Rhaegar surrendering for the sake of "justice" is not noble at all. The rebels were fighting to bring down his family which includes Elia and the children. Surrender endangers them. Can you blame him for picking the option that gives them a chance? It's not like he could have predicted that his defeat would lead to their deaths.
Who said suing for peace doesn’t give Elia and the kids a chance? Imprisoning Aerys earns Rhaegar brownie points for offering the rebels a semblance of justice, and it also works to distance him from any culpability in his father’s crimes. Which leaves his own absconding with Lyanna but while it’s a huge thing, it’s not enough to continue a war for, especially once Rhaegar guarantees Lyanna’s return, safety and well-being. Sure, Robert would want to off Rhaegar right then and there and burn everything to the ground in revenge, especially once he finds out about the pregnancy and that she left willingly, but the combined efforts of Ned, Jon Arryn and Hoster Tully should be enough to impede that, and Robert alone can’t continue the war if the others won’t play.
If Rhaegar overthrows his father and asks the rebels to the negotiating table, he forestalls any attempt on his or his family’s lives. The rebels can’t afford to strike against the remaining Targaryens - compromised largely of innocent women and children at this point - during peace negotiations or violate the terms of said peace once it’s set, not if they don’t want to utterly tank the image of the rebellion and the understanding that they rose in defense of the law and social contracts. Moving against Rhaegar or his family under these circumstances paints the rebellion as a simple power grab, losing it its legitimacy and a good deal of support. A peaceful end to the war also prevents any sacking from happening, minimizing the chances of someone slipping during the chaos to strike at the royal family, currently guarded by members of the Kingsguard if not already packed off somewhere else for safety.
Better yet, once Rhaegar wrestles control of King’s Landing from Aerys, he can easily ensure Elia and the children’s safety even before reaching out to the rebels. He can put them on a ship to Dragonstone immediately, just in case the peace negotiations fall through. Hell, put them on a ship to Dorne. I’d like to see Robert commit political suicide and bleed whatever support remains to him trying to invade Dorne to kill their princess and her two toddlers.
The rebels were fighting to bring down his family which includes Elia and the children. Surrender endangers them
I’m generally not too moved by the argument that Rhaegar was backed into a corner and just had to fight to save his family for several reasons, the most prominent of which is that the whole situation is of his own creation. The fact that rebellion was against all Targaryens instead of just Aerys is Rhaegar’s own doing so arguments about how Rhaegar had no choice don’t really impress me, not when he was the one who put his family in danger in the first place. He did have a choice, and he chose to humiliate Elia, disappear with Lyanna and create a political crisis that he had all the information required to know would devolve into a disaster. He doesn’t get to claim that he had no choice when his actions are what put his family in that position.
I’m similarly unmoved by arguments for Rhaegar’s concern for Elia and her children. Rhaegar humiliated Elia publicly more than once. Heleft her and his children to Aerys’ mercy when he disappeared for months, knowing what he knows of his father’s racism and paranoia. And even when he returned to find Aerys keeping his wife as a hostage for Dorne’s loyalty, he took three of the four remaining Kingsguard, including Elia’s own uncle, to battle and left Aerys, Rhaella, Viserys, Elia and his two children under the protection of a seventeen years old boy who he knew was being kept as a hostage himself against Tywin. He left three Kingsguard, including the Lord Commander and the Sword of the Morning, to guard Lyanna but the only adequate protection he leaves for Elia and his two children is Jaime Lannister? Why wasn’t he concerned for Elia and the children when he abandoned them to his father’s whims or when he left them behind to act as hostages? Why does his oh-so-consuming concern only become relevant when it’s needed to put a positive spin on him continuing the war without a care for those who would fall as a result of his own transgressions?
