https://faq.usps.com/s/article/Refuse-unwanted-mail-and-remo...
I'm pretty sure that both EDDM and specific bulk mail senders can be blocked.
There was a long-standing rejection applied to pornographic materials, based on the recipients own assessment based on "I know it when I see it", though that loophole may have been closed.
From the old Junkbusters site, there are a Form 2150 and 1500 which can be filed against any sender.
https://web.archive.org/web/19970713104642/http://www.junkbu...
I'm only finding the form 1500, here:
https://about.usps.com/forms/ps1500.pdf
You can also directly contact bulk senders through the DMA mail preference service, Valpack, RedPlum, and others. See one listing of these here:
https://www.huffpost.com/entry/how-to-stop-junk-mail_n_5b27b...
The From 1500 is the take-off-and-nuke-it-from-orbit option, however.