Living Richard dreamed of being a hero and wasn't afraid of becoming a monster because he trusted John and Geoffrey to slay him if need be. John would rather have nothing to do with the hero/monster dichotomy. It turns out Richard did become a monster, and pretty much everything turned out the way John warned him it would, so Richard thought the only thing that could save him was a long round of punishment in Purgatory.

Later, Avenger John killed Berserker, Rider, and Saber Richard. They're all different facets of the real man, but every single one them was symbolic of all the issues John had with what the epics turned his brother into, further motivating to lash out against the world and its storytellers. None of those instances are John trying to stop Richard from becoming a monster. It's too late, so effectively John was only indulging in his brother's punishment-seeking fixation.

But Saber's death was inconvenient to Pale Rider's attempts to protect Tsubaki, so he was granted the Purgatory he sought and was remade into his 3rd Ascension borrowing from Pale Rider's own Ruler Saint Graph. In his personal Purgatory, Tezcatlipoca calls him weak of spirit for actively seeking punishment in his search for salvation, which is a thing Richard comments on as a lesson learned, but I think the important part is what Richard doesn't know. "Ruler" Lionheart fought for the extremely personal reason of stopping his brother from doing something extremely suicidal, and in that, he served his purpose as a tool to save Tsubaki despite being wholly unaware of Tsubaki's situation. Richard here was a hero organically and unknowingly instead of following his usual desperation for by-the-books heroism.

The post-climax has Richard seeking a real fight with John, after three instances of his suicidal tendencies allowing John to kill him without resistance. He's embracing who he is and showing off his liberated self, perhaps not for himself but for a brother going through the same pain. Tezcatlipoca's admonishment gets the credit for it, but having just fought to stop John from also intentionally dying of guilt for Richard's sake, I think Richard can actually see the metaphorical mirror there. If John is a mirror, it was only being freeing himself from his own constraints that Richard could free John from his.