Its an interesting question, but I think an equally valid one is what would it have actually taken for Rhaegar to win at the Trident? While Rhaegar's death at Robert's hands was a significant blow, the crown's Dornish forces (some 10,000 men) had already been broken, Prince Lewyn Martell, at least three of Rhaegar's own bannermen and Jonothor Darry of the Kingsguard were all dead and Barristan Selmy had been gravely injured and captured before Robert and Rhaegar even faced off. Let's say Rhaegar cuts down Robert. That doesn't cripple the Rebellion leadership because they've still got Jon Arryn, Eddard Stark and Hoster Tully on the field of battle and Stannis next in line to succeed his brother as leader of House Baratheon. Meanwhile Rhaegar's still lost a good chunk of his men (who were said to be not nearly as battle-hardened as the rebels) and almost all his top commanders. Even though he has survived, I think Rhaegar withdrawing his army from the field at that point is the only rational outcome. Best case scenario coming out of that is that the Mad King still tries to burn the city and Rhaegar has the influence to depose him. This makes Rhaegar king and with the Lyanna-obsessed Robert dead creates an avenue to sue for peace. Presuming that Rhaegar set aside Elia so that Lyanna would be his queen and offering up the deposed king to be tried and punished by the rebels, the Targs might be able to hold onto the throne. More realistically though, the Mad King doesn't wait for Rhaegar to return and its still Jaime who has to kill him so there's no scapegoat to easily offer up and Lyanna still dies in childbirth not too long after with accusations getting thrown around as to whether it was natural causes or murder disrupting any chance at peace. About the only thing I see Rhaegar beating Robert at the Trident doing is buying a little more time for the Targs to put contingencies in place. They're still going to get stabbed in the backs by the Lannisters. The only real difference might be that with some leadership to rally around there's a real siege of King's Landing before Rhaegar and his family die and we end up with Stannis or Lord Tully or Jon Arryn as king in Robert's place, each with their own inherent problems holding the realm together until something finally shatters the peace. The Rebellion ended up being so much bigger than Rhaegar, Lyanna and Robert that I just don't see much that Rhaegar would be able to do to halt the inertia of it. Blunt it a bit maybe, but I still think we'd end up mostly where we are now, just with slightly different players and a different spark (but probably still struck by Littlefinger) setting it all off.
