For me, the main advantage of the Public Uploads page is to easily fetch the UUID and checksum of the public uploads.
The main example where this is useful for everyone is Crust-DFT. It has several input files that already exist as public uploads (and are essential for a quick run of the module) , but it is very hard (maybe impossible?) to find their UUIDs and checksums. Having a page that shows all the public uploads makes this search very straightforward.
Also, from the latest MUSES meeting, we know there are people interested in having a centralized place to have static EOSs uploaded (especially for heavy-ion, since NSs have compOSE).
I do believe it can become messy if people start making lots of tables public. We could go back to our last conversation about it and make another type of upload. We could differentiate between Public files and Shared files, where Public files are very limited and uploaded by admins, and Shared files can be used by anyone, but the UUID and checksum have to be given person-to-person.