There are only a handful of words left over from Japanese, they stuck because they're either proper names, or concepts whose English equivalent is not quite the same thing (or in some cases with the original translation just plain wrong).
For Ama no Murakamo: Changing it would be like calling Excalibur "Battlebreach" or something similar. Heaven's Cloud is a very rough translation but is equally meaningless to a person unfamiliar with the actual sword, so what's there to lose?
Fangtian Hua Ji is a legendary class of polearm that appears in the Romance of the Three Kingdoms, Flayer conveys nothing of the meaning (which is something like "Heaven Pointing Spear"), so again, I'm not sure anything of value is lost.
An omamori is an amulet, but an amulet isn't necessarily an omamori, much like ninja <-> spy. There are plenty of other choices for amulets the designers could have made, but seeing as they chose an omamori I think it's right to honor that choice.
I figure the majority of people don't have regular names in the FF7 universe, so any changes are probably getting it closer to what was originally intended.
Yeah Zack was always an odd one, I mean we have Cloud, Tifa, Aerith/s and...Zack? Really?