That is very interesting. Thanks! Looks like you can submit it without an email address. Facebook can provide this because they have a whole team probably just responsible for responding to these requests.
As a first step here my thought is to improve the About page, to move the contact email address up nearer the top and to update the language to make it more clear that anyone is welcome to use it to report a problem with the site which might include reporting illegal content that should be taken down, using DSA friendly wording. The About page also has links to the TOS and Privacy notice, if the site has set these up, so sites are covered but it requires reading and is not necessary quick and easy to find how to report a problem with content on the site. If the site has full contact details specified, then more of that can also be provided directly on the About page, like you see on the “Impressum” page on German-speaking sites.
Beyond that I wonder if there is more we can do to make the About page more discoverable in the UI for logged out users. Looking at meta today, logged out, I don’t even see the link to the About page because the first section is not shown to logged out users here. Maybe we add a link to it to the sidebar somewhere?
And finally, returning to the OP. Having seen the way facebook handles this I do see the value in letting anons also flag posts using the review system logged in users have access to. It could really help communities to stay clean and comply in practice with DPA.
But if we did that it would have to have all sorts of anti-abuse mechanisms built in. I can’t see us doing that anytime soon but it might not be a bad idea to collect ideas.