The Files App does not exactly work like Finder. It gives you access to a central file store that an application must support before your files show up there. It does NOT give you the ability to browse the iOS filesystem.
Funnily enough, one of the biggest issues I have observed with my parents using a desktop computer is "well where did that thing go that I was looking at yesterday".
Naked filesystems are intuitive to us as power users because we are in a mindset which many more casual computer users aren't. We understand that it's a hierarchy and that files have formats and extensions and file type associations and a whole list of technical details as to the how and why.
On the other hand, there are plenty of people who have no idea about this stuff - they will be thinking about the application they were using at the time and will expect that things they have "saved" are somehow associated with that application. They might not even associate a contact card or a photograph with being a "file"!
I feel like the iOS Files app makes a decent attempt at bringing features that we power-users enjoy - like tags, search, online storage - into an ultimately simplified model that is cognitively compatible with a much wider spectrum of users.
The ideal user interface to a filesystem is one that actually foregoes the idea of "files" (because formats and file type associations and extensions and things aren't intuitive to everyone) and instead treats photographs like photographs and contact cards like contact cards and emails like emails and webpages like webpages. It seems Apple are striving towards that. Did you notice in the keynote that, when dragging and dropping photos into an email, they were actually represented as photos and not as file icons?
I'm not saying it's a bad thing. I agree that they are approaching this the right way. It's just not the "Finder for iOS" that many are calling it.
The president of my company is one such person as you describe. He has no idea. He puts everything on the desktop, because the only way he knows of opening a document is to launch the corresponding application, and then File, Open the file on his desktop. In other words, he treats his Mac like an iPad. We have tried to break him of this habit, to no avail.
