I can have a go at explaining the thinking behind the way that iPhone stores data, and why 'saving files on the device' is not a meaningful way of working.
I'll try to simplify the explanations enough so that you get a taste of what I'm talikg about, at the expense of a little bit of accuracy). I will also ignore the possibility of storing files in iCloud for this discussion The 'Files App' in iPhone is really for iCloud users.
The truth is that the iPhone has a different way of doing things as opposed to the classic model of computers for many decades. Yes, behind the scenes there is a folder structure similar to that with which you might be familiar on your desktop PC, but that is hidden from the user of an iPhone as it is irrelevant.
The way that 'Apps' work in IOS (the iPhone operating system) is that each app stores the files that are relevant to it with itself, in a hidden data folder alongside the program files that make up the app. Each App can only access the files stored with it - it cannot access another Apps files. In many cases files are only useful on the app with which they are associated with, so this model does not hinder use if the files. If an App is deleted, all of its files are removed as well so that there a no orphaned files lying around.
I did say ...'in many cases'.. above. Some files are relevant in more than one app. Consider a photograph. You might want to email it to someone, or open a pdf file received in an email within a specialised PDF reader. In those cases an App has to be told to share a file out to the other App. You might select a photo in the Photos app, tap on the share button (the square with the arrow pointing up) and select 'mail'. The Photos app then taps the mail program on the shoulder and hands it the photo. The mail app can then open and offer the user a new message form with the photo attached. The Photos app had the photo in its storage and had to give it away to the other App.
So really you can do it all, it's just a different way of looking at file storage. Once you get over the shock of having to work a different way, it actually makes sense. Each App has exclusive custody of its own data, an App cannot root around in files (belonging to another app) that you did not intend it to see, and as Apps and their data are kept together, the phone does not suffer from gradual degradation as PCs do with bits of data stored here there and everywhere... The phone stays 'tidy'.
You talk about 'saving files on your phone'. In reality apps DO save their data on the phone - they just hide the technicalities of where from their users. In this way of doing things, it is irrelevant to the user.
Files are transferred between the phone and your PC using iTunes. Again in iTunes, you give or take files to/from an App and it handles the technicalities of where that file is stored on the phone.
Yes it's very different - but it is much more secure and aids manageability of the device immensely.
Apple have never been afraid to do something different - this is one of those cases, but in my opinion they got it right.
