It does have that through portals:

https://github.com/flatpak/xdg-desktop-portal

If you Flatpak a Gtk+ 3 or modern Qt application you get portals for free. E.g. I packaged a Qt application and I am not sharing the home directory - when the user opens a file it uses the Qt/KDE portal (similarly to macOS, ChromeOS, etc.).

As far as I understand the problem is that portals are only available for Gtk+ and recent Qt versions. Some of the applications that the posts mentions use toolkits that probably don't support portals (Java JDK, wxWidgets, etc.).

The situation for Linux is a bit different than e.g. macOS, where practically everything uses Cocoa and Apple could just throw the switch.

So, for applications that do not use vanilla Gtk+ or Qt they still need to make the home directory visible or they would not be Flatpack'able.

I have a fuse filesystem that shows different users different views of the filesystem, as a basic example.

The problem is rather caused by filesystem layout conventions. I think that a better solution would be to split user home directories into two classes of files: data (that is, files that the user typically wants to see and work with as part of the normal workflow) and "user profile" kind of stuff (.bashrc, configuration files, etc...) that should be "privileged" and require special access rights. These might require interactive confirmation before write access is granted (similar to the split user accounts in Windows with UAC). However, I wonder if these sets of files can be separated cleanly. Marking files as "privileged" should be doable using extended attributes, though.