1. The enhancement bonus to Armor/Shield/Natural works because it's adding a bonus to a bonus to determine the magnitude of said second bonus.
2. The enhancement bonuses are effectively being laundered into armor, shield, and natural armor bonuses.
3. Weapon enhancement bonuses to attack and damage rolls stack with the "enhancement bonus" from Belts of Giant Strength in a similar manner, because the giant strength is laundered through your Strength score into an untyped bonus.
4. However, adding multiple luck bonuses to initiative and to Dex won't make them stack, because it's still a luck bonus being applied to the final check.
5. It would work if initiative modifiers were defined as modifiers to initiative checks plus your total modifier on Dex checks, since any bonuses to Dex checks would be laundered into an untyped bonus with that writing.
1, 2, & 3 disagrees with 4, not off to a good start there.
5.
Differences must be defined?
Enhancement Bonuses
Enhancement effects make your armor better.
According to Armor Class rules, enchantment bonuses improves armor.
Not enchantment bonuses improve your shield bonus.
Not enchantment bonuses improve your natural armor.
It could mean enchantment bonuses improve your armor's bonus.
It could mean enchantment bonuses improve your armor class.
If it means armor worn only then boy we sure have redundant items that should have never been printed. Shields, pure fluff.
If it means your armor class, since enchantment bonuses cannot be stacked, only one such bonus can ever be applied.
Now we do have text printed for enchantment bonuses to armor, shields or natural armor despite enchantment being one and the same in the eyes of Armor Class rules. We even have printed examples, officially ran games, intent, even logic would agree you can stack them as well. On the same exact token. We've got +A to B & +X to Y being combined. It you firmly say they are one and the same then based off your opinion I can say White Raven Tactics gives +20 to dexterity checks, which seems to go against intent, pretty much granting immunity to trip while giving one heck of a Hide/Move bonus.
Either way you argue it.
A. Extra initiative by treating initiative as a separate entity from dexterity checks thus stack ability.
B. They really are one and the same therefor initiative boosts apply to all dexterity checks.
I win. It's great.