and the shutdown of basically any kind of public forum on a small site since it is going to be nearly impossible for small entities to comply with regulations.
Legally, perhaps it could be sufficient to include a check box saying "I certify that I am the copyright holder to everything I upload". Compare with the way EU handles the cookie law and GDPR consent click-yes.
You're joking here, but a politician in Poland, when asked about how shall a popular link sharing platform (wykop.pl) deal with submissions, of which there are 100k / hour in peak times, actually suggested that "users should know not to upload illegal materials".
The last sentence threw me off (about certain content not being covered). If it was just your first paragraph, I would have thought it was sarcasm. And I was tired.