Some equipment in game also have that property, you need to think of it as a one time use consumable, and the properties transfer with the appearance when you remodel. If your armor already said on it "Can only be used once to remodel appearance" that's for that armors appearance. If you were to put it on any other piece, be it another "Can only be used once to remodel appearance" piece or one that allows infinite remodels, It will still say "unable to extract appearance" cause you used the 1 chance it had of remodeling. If you were to remove the remodeled appearance that you just put, your armor will return to its original appearance and with it its original property aka "Can only be used once to remodel appearance". I hope you understood cause it's a pretty simple mechanic.
Another scenario is when you put a skin that you can remodel infinitely on an armor that states on it "Can only be used once to remodel appearance", the result is that it will not say anything on it, cause you replaced the appearance with a skin that has infinite remodels, and you could reuse it on something else but, if you reset appearance to its original one it will go back to saying "Can only be used once to remodel appearance".
The phrase "Can only be used once to remodel appearance" would have no sense if you could remodel that skin infinitely, cause there is a counterpart where you can reuse the skin infinitely and that property on those item is empty (there is even some rare items where it says on them "Cannot remodel" from the get go). The one use thing is made that way for shop items (for obvious reasons) and even some in game equipment and that is just how the devs aka ncsoft made it and it's been like this since forever.
I also doubt that they could modify it here cause they would need some good programmers to modify those item properties without breaking anything, Items have IDs etc... They need to know the engine and other stuff. The other server you are talking about I wonder if its the same one, but they also added items from further updates, they even made some custom npcs and other features. This server only have admins/GMs and they only have access to commands for that. (also that other server economy is busted and they have pay to win in its shop and its a worse case than having skins only be used once).