This is working but the downside is that the link is very long and percent-encoded which makes it difficult to read. Would be great if documents could also be added as file links or if we could specify a display name for the custom field hyperlink.

mowo, it could be done as in a UNC path (\\server\share) however, the problem is the context under which the application tries to open the file. you might then get into delegation issues etc. Also, as the app transitions to the cloud eventually like everything else seems to, opening those would be much more challenging.
I feel your pain as I wanted to do something similar.

Using custom hyperlink fields with a file link and a UNC path (e.g. "file://server\dir A\dir B\file.pdf") can be used as a workaround for assets. However, this is not working for e.g. software licenses. Those entries support the upload of documents but don't have custom fields. Would really appreciate if file links would be supported somehow.