And all at once, the universe groaned.
Not missing out on core cannon, you're ignoring that arbites do in fact answer to Terra they also have various branches that do more than just collect Tithes from planetary governors because anything that should be cut and dry in the imperium gets muddled extremely quickly. It's how and why the guardsmen for some reason decided it would be a great idea to use ratlings as snipers.Ah your missing out on core canon.
Arbites is a technical term.
Adeptus Arbites - Warhammer 40k - Lexicanum
You mean any random police-esque force.
That has a whole host of other issues.
(I could of thought of that but to be fair googling arbites, provides 0 non- adeptus-arbite responses for 40K)
But the actual arbites, everything I said for them is true.
Each branch is pretty subject to whatever that planet they're stationed on happens to really need to make sure things are orderly. This can be open to very liberal interpretations. It's one of the reasons why the arbites work with the inquisition so often.