I think OP means that the community feeds a database using a platform they have no real control over, as the source code of the website/WebApp is not public.
However it is good to remind people that ProtonDB database is published under the Open Database License ODbL at this GitHub repo. To me having the db under an open license is more important than a WebApp (especially now that anyone can build such a website in a probably insecure way, using a 20$ monthly LLM subscription).
I haven't digged into the db myself, maybe it does not come with the comments and so and only the borked, silver, gold, platinum labels.
So yes the website doesn't seems to be open source but the database is. So anyone could rebuild an alternative from its database (which is probably the most precious part of ProtonDB). If nobody already did it yet, it's probably because no one felt the need for, as ProtonDB already offer a valid, great and free user experience with currently no reasons to distrust the project.