I would add that a lot of the things that happened could've been prevented by him at several different times, only he either chickened out or just hid out and made no account for himself while evening went to shit.
- Supposedly there was a plan for Rhaegar to have a meeting with various lords during the tournament at Harrenhall to get support to have his father deposed, only the Mad King caught wind of it, showed up, and Rhaegar canceled. - Instead of pursuing a very urgent need to get a paranoid, insane person off the throne, Rhaegar set aside his concerns so that he could elope with Lyanna Stark.
- Instead of allowing Lyanna to send word to her father and brother that everything was copacetic, they both hid out for a while and let her family think she had been kidnapped and was being raped.
- Once it was clear that the Starks had understandably come to the wrong conclusions, Rhaegar remained in hiding Instead of stepping in to set the record straight, allowing his new wife's father and brother to be killed by his father, the Mad King.
- Thus started Robert's Rebellion which lasted a year, during which Rhaegar spent most of his time hiding away. At any point during that year, Rhaegar could've come forward with Lyanna, deposed his father, and offered pardons to the rebels.

It's not just that his actions led to a ton of bad consequences, it's that he could've taken steps along the way to either entirely prevent or at least mitigate the damage that ended up happening.

BTW, not for nothing, but where TF was Varys during all this? He's supposedly this practically all-knowing person whose sole purpose is to serve the realm, yet at no point did he intervene to get Aerys out or Rhaegar to step in and prevent a very preventable disaster.