Uuuhh.. That's -just- what we need, a religious nut as the High King. Thank you but no.
Tyrande leads the night elves and the religion, it's basically the same thing, except one's a racial leader and the other is the racial leader and might become the High King after Varian.
Anduin is far more stable than King Chin. Also what would be wrong with that scenario?
Tyrande and Velen only hold religious sway over their races. The fact they are also their races leaders doesn't give them the authority to push their views on the other races. Three of the races follow a form of the Light already. The humans, dwarves and Draenei. The Worgen probably do somewhat, but they are very outnumbered by the humans. The gnomes and panderan probably don't care, which leaves the Night elves as the odd race out that definitely worships very differently.
Anduin, as the High King, would be in a position to put forth the Light as the religion of the Alliance. He's stable now, sort of, the boy needs a good solid dose of reality to wake him up out of his foolish idealism. But if he is the Archbishop (head) of the human church, as well as the High King, he is literally in the position of being able to make what he says/wishes, come true. He would be holding the secular over the Alliance and spiritual power over three to six races.
There's the saying, power corrupts and absolute power corrupts absolutely. The temptation for him to abuse his power would be immense.