Specifically 3 reasons:
1. Some elementals (if using the GPA alone or in conjunction with a PT) are immune to magery. Shadow Elementals and Valorite elementals. The Anatomy & tactics are for DI for the mage weapon that is your fallback position for these, and if course Enemy of One, consecrate Weapon and Divine fury boost combat bonuses. For that matter, often mage weapons drop the elemental faster than summons, when used with chivalry.
2. Chivalry allows you to heal without hauling regs/bandages around, and without having to use LRC (jut got to remember to tithe). Traveling can be done this way, as well, so if something goes horribly wrong and the insurance bug hits, you can sacred journey to resupply to go back for your stuff.
3. When you're overweight and walking back to a house or bank, you can chain-cast divine fury to restore your stamina.