I just got my X 2 days ago. My system size is a whopping 47GB. Apple so far has no explanation but admits it should be 6-8. I do have 39,000 photos optimized in the cloud. I also noticed the System size consistently expanding while photos were syncing. I will try your suggestion.
"System" is mostly deleted data that hasn't been overwritten. "Other" is a catch all word used for data that doesn't fall into the categories listed such as Apps, Media, Photos, etc etc. The deleted data from "system" on the NAND falls into the "other' category.
With flash storage the data is stored as pages and the pages are stored within blocks. The problem is the actual delete function operates on a block level. So if you delete data (pages) but the block contains other data (pages) the data you don't want needs to be moved. This not only requires time and a place to put the data that isn't going to be deleted (the reason a full SSD becomes slow) but wears the finite number of write cycles the NAND has.
Knowing this you can literally (albeit very carefully and intentionally) add and remove "system" and "other" (at the expense of actually using the space) on iOS. I did this by removing the two movies from the TV app I had and than adding two movies that are slightly larger to completely fill the space plus a little more with similar data.
So the more you delete the more "system" and thus "other" space is consumed. This includes taking a pic with your iPhone and it being removed from the iPhone after it syncs to iCloud. Installing things doesn't always overwrite things either since it would depend on the pages marked for delete and the new data being stored. Regardless once the storage is getting too full with "other" caused by "system" it
should force its use with new data. If not I would see if the "other" is actually something other than "system".
I can't find any data on how the kernel for iOS handles garbage collection, wear leveling and TRIM however it is going on in some way or another. Google announced and implemented TRIM into Android 4.3
I believe, so I would imagine Apple has it implemented too in some form as well. I'm going to run a little experiment though, I just deleted those movies back off my iPad so I currently have 8.09gb of storage being used by "system". I rarely use the iPad so I should be able to tell if a TRIM command is ran.
I'm not exactly sure why Apple shows this data in iOS to the user. If I were to guess it would have something to do with encryption (since its still there it needs to be encrypted its still shown) but thats just a WAG.
HTH a little.