Multisites with shared files folder – good or bad idea?
This should not work. Managed files should be automatically removed once there are no more entries in the file_usage table for them. I see you say that it's not happening on your setup, but maybe that's a permission or some other issue. That's not how it's supposed to work.

I'm curious how you plan on this working, in any case. If you're using file fields, then Sites B and C would have no way to know that you uploaded a file to Site A, so how it is useful? You say that you're using a file manager. Is it like IMCE or something where you are just browsing the files by directory? If you upload a file through something like that, it wouldn't get an entry in the files_managed table, so it would not be automatically deleted. That would make sense.