Fighting insanity.
The under ground fighting pits had been the means for which David had fought off insanity. He didn't care for the pain, in fact it proved to be what a sanity saver. The pain had given him something to focus on other than the emotions that threatened to destroy his mind. Proving to him that he was still alive. not all those fights ended in his favor.
Still After his control metal had been knocked out from that train heist, his body had been reset to the point of its initial bonding had been due to regeneration. He has spent years in war fighting horrible minsters that knew no limit to their evil. The anger, pain anguish, he had built up a resistance to the hormones that caused them. Allowing him to adjust. Full body regeneration had undone that natural adjustment.
The fights had been a balm. The pain some sort of counter balance to show he was still alive, still felt pain. Still had something to contribute. It was never about the money. It was about not devolving into a Hotheaded Psychopath. Chronos had stolen everything from him. He refused to allow them to steal his sanity and dignaty from him.
Wandering the World Tree had allowed him to see plenty of sights and sounds. Sticking to the gutters and gettos had allowed him to hide. Perhaps it was time for him to find some purpose in the world tree. He had anything open to him, once he was done with the next few fights he learned about, he'd consider looking for something to do with his life.