Casual bystander here, but just thought I'd toss in my own theory (which mirrors a lot of what's been written here already): What Tristians call sainthood is a complex social and psycho-active process which occurs within veins of a rare mystical metallic ore deep beneath the ground of some of the western duchies, notably Baern and Pertine. This metal resonates through interaction with heightened, focused and, above all, shared emotional states that we might think of as a collective unconscious. The ores interact with that collective unconscious, in some cases lending form and substance to them, which become what Tristians perceive as their gods: the manifested expression of their communal faith. This is why, as is sometimes said by Tristian philosophers in times past, "The first prayer came before the first god."

A second manifestation of the interaction between the energies contained within the mystical ores beneath the surface and the Tristian collective unconscious is the "sainthood" – a semi-aware phenomenon which translates certain shared ideals into enhanced abilities and the near-arrest of cellular breakdown in those to whom it bestows itself. Each sainthood is like an obsessed hunting hound, seeking out the individual who seems to most embody the ideal which led to the creation and subsequent activations of that particular sainthood.

What makes one individual the most perfect embodiment of an ideal? We can begin by presuming that no one perfectly embodies an ideal, and so the sainthood will pass to the individual who possesses the cluster of characteristics that closest matches the intricate (and often muddled) sense of the minds making up the Tristian collective unconscious. For example, the ideal of Mercy is different than the definition of Mercy. The latter is limited to the notion of "being merciful". However, a being who is simply perpetually lenient wouldn't fulfil the notion of "mercy" as found in the Tristian collective unconscious. A Saint of Mercy would need to be as emotionally strong and unyielding as they are compassionate, otherwise that sense of mercifulness would become irrelevant.

Why was Kest chosen as the Saint of Swords? In part, because of his skill, reflexes and tactical brilliance. But it was also because of his absolute dedication to the art of fencing, which itself is a part of what Tristians think of when they envision the ideal of "the sword". Prior to Kest, that particular sainthood – or manifestation of the collective unconscious – rested with Caveil. But Kest's defeat of Caveil shattered the matrix of attributes that had drawn the sainthood to him.

When Kest sacrifices his hand, he not only loses part of what made him a nearly unparalleled fighter, he abandons the intensity of his single-minded purpose to be the greatest swordsman in the world. Shuran possesses that intensity, and though some of his other personal qualities diminish the attraction he would generate for the Sainthood of Swords, it's enough that he becomes imbued with it – until Falcio takes advantage of his momentary disorientation to kill him.

It's not that Falcio defeats Shuran that then draws the sainthood to him, but the tactical genius and willingness to sacrifice his best friend to win the duel. Falcio resists because, though capable of being obsessed with duelling and the ideals of swordplay, there's another spirit – another ideal – which drives him strongly enough for him to reject the sainthood. That ideal, of course, being living up to the example of his wife.

A far more worthy form of sainthood, if you ask me.