It would be nice if core files, plugins, themes and uploads respectively would be kept separate of one another - both as locations and as objects.
That would make it much easier to move servers or switch between versions in case anything goes wrong.
Several websites could share a single install. It should also make it possible to specify different log-in paths - on subdomains or even different domains.
It would probably take some amount of symlinking and hooking into the existing code to preserve backwards compatibility.
example of directory structure:
*each with their own config.php etc.
This is an interesting idea, it would also make it easier to update multiple sites at once, while avoiding some of the inconveniences of a full multisite installation.
Mike Schinkel and I have discussed similar setups. I'll ping and see if he wants to comment here.
I also think that in general, making it possible to have a more flexible file structure is a good idea. See https://docs.classicpress.net/installing-classicpress/installing-with-composer/#after-installation and the links out to other resources from there.
On first impression, my first reaction is "Yes!"
I'd like to hear more about what you envision, i.e. specifically what you envision an implementation to look like.