I'm pretty sure theocracy just means the nation and government are ruled according to the religion. Religion in turn does not mandate worship of a deity.
And Mika sent himself because "I have no desire to watch Spira die." I guess it is cowardice in that he was afraid the world was doomed to destruction...
Also you should read the origin of the Yevon faith. Maechen tells it to you if you find him on Gagazet.
Quote:
Maechen
"Rumors flew in Bevelle about Sin's sudden appearance."
"They said that the people of Zanarkand became the fayth, that they had called Sin."
"And that the man responsible..."
"was none other than the summoner Yevon, ruler of Zanarkand!"
"Yes, the lord father of Lady Yunalesca."
"On the eve of Zanarkand's destruction, Lady Yunalesca..."
"had fled to safety with her husband, Zaon."
"Later, the two used the Final Summoning to defeat Sin."
"Yet the people of Bevelle still feared Yu Yevon."
"It was to quell his wrath that they revered him, and first spread his teachings."
"And so were born the temples of Yevon."
"I suppose it's possible Yunalesca had planned it that way from the start!"
"A fair trade, she defeats Sin in exchange for her lord father's honor."
"Of course, there's no proof. No, the facts are lost in the mists of time."
"And who'd admit Yevon was an enemy of Bevelle?"
"You can bet the temples had a hand in covering that one up!"
"And that, as they say, is that."
Final Fantasy X | 10 | FFX | FF10 - Script - Maechen - FFWA
Bevelle did all that stuff because from the first they were trying to avoid Sin killing everybody. Mika's complete despair when he hears Yunalesca is defeated is proof enough he was not just some tyrant who ruled over Spira because he was in love with power. He did it because he sincerely believed Yevon was the only way to keep the world even vaguely well-off.
If you look at it, all the villains of the game had their own idea of how best to "save Spira." Yunalesca echoes many of the same sentiments as Mika and Seymour took their logic to its natural, extreme conclusion.
Mika:
"Men die. Beasts die. Trees dies. Even continents perish. Only the power of death truly commands in Spira. Resisting its power is futile."
Yuna:
"All the people who have opposed Sin... Their battles, their sacrifices, were they all in vain?"
Mika:
"Not in vain. No matter how many summoners give their lives, Sin cannot be truly defeated. The rebirth CANNOT be stopped. Yet the courage of those who fight gives the people hope. There is nothing futile in the life and death of a summoner."
Auron:
"Never futile but never-ending."
Mika:
"Indeed that is the essence of Yevon. Yevon is embodied by eternal, unchanging continuity, summoner."
-------------------------------
Yunalesca:
"Hope is...comforting. It allows us to accept fate, however tragic it might be. [...] Yevon's teachings and the Final Summoning give the people of Spira hope. Without hope, they would drown in their sorrow."
And then Seymour sees that this horrible "false hope" life that is perpetuated and unstoppable by all accounts as being far worse than death itself. As Yunalesca tells the group, "it is better for you to die in hope than to live in despair. Let me be your liberator." That might as well be Seymour's motto.