It misses the forest for the trees.

The overwhelming majority of the populace of Europe during the period under discussion (800-1200AD) was subject to the direct justice of their liege lord. If Baron von Snufflebottom said you were guilty, you were guilty and your head would be off as soon as they found an axe. The only people subject to trial by ordeal were Baron von Snufflebottom and his posse, and the ordeals were leverage in the power struggle between church and state. If Baron von Snufflebottom decided that the local bishop was living too large off his tribute, he might get his buddies together to reef down on the bishop. If the bishop could get his posse together in time they could find a quisling to accuse Snufflebottom of witchcraft. Then it came down to who has the juice - Snufflebottom can toe the line and be innocent of witchcraft, or he can make this a thing and stick his hand in boiling water.

It wasn't an effective test of guilt, it was an effective test of power. And this is why The Crusades happened, Martin Luther happened, the Reign of Terror happened, etc etc etc. European history is one long pissing match between church and state.