Fair enough, but hypothetical rebuttals do little to nothing to diminish the example I provided. You can claim that Commoners will grow tired of anyone who lived out their life, but there are quite a few leaders who were well liked, all the way in their old age. Let's use the former leaders of House Stark as an example. It takes a great deal of respect to be dubbed King of the North, which is a title that has been held by several heads of House Stark. They're known for being fair, and just.

I will say that Rhaegar didn't start the war. There are mysteries surrounding the whole ordeal with Lyanna and Rhaegar, but Rhaegar did not start anything. The war was instigated by Robert Baratheon, Ned, and Jon Arryn, which is why it was called Robert's Rebellion or the War of the Usurper. There are several reasons why a war was instigated, all of which are because of Mad King Aerys. It seems like you're ignoring key events years prior to Lyanna even going missing. It was Aerys' actions that pushed everyone over the edge. Brandon had no idea where Rhaegar was. Assuming that he was at King's Landing with Lyanna, he went there and threw a fit. Aerys had no idea where his son was, but he was pissed and claimed that Brandon was part of some conspiracy to kill the Prince, and had Brandon and Rickard killed.

Again, we don't know if Rhaegar abducted Lyanna, she could've went with him out of her own free will. The point is that Aerys' had a history of going 0-100 and mistreating everyone. He treated his own wife like shit, so her paternal house is rightfully upset at that. He treated Tywin Lannister like shit, a man who served him loyally as Hand of the King, and he may have been a bit touchy feely with Tywin's wife.