"One simply can't avoid using the filesystem view for operations like moving or copying files"
from where to where?
if you mean between storage devices (e.g. internal storage and a connected USB stick or an SD card) that is already supported in the Files application. each device has an entry at the top and you can drag things to it.
if you mean between directories on the device, the question then becomes: what is the use case? the valid use cases we've come up with are so far all in the edge case, and so we do not optimize for it.
you can go into a specific directory, however, by running a search for the directory and then pressing/clicking on the folder in the results. voila, hierarchical browsing begins. it just isn't what the UI is optimized for in terms of common usage .. because for common usage that mechanism is slower and less useful than the metadata system.
design is hard. it means stepping back and examining the "why" behind the things we desire; identifying the use case(s) behind the mechanisms; challenging ourselves to come up with better ideas rather than default to the least-worst thing we already have. that all requires a lot of thought, a lot of discarded ideas (few of the ideas in Active were our first attempts :) and a high amount of domain knowledge. so it does not surprise at all that the above is not immediately obvious .. until one uses the results of that process and finds it actually works ;)