I feel like the whole time this was being argued and passed, everyone in power just considered the internet to be the major social media sites and never considered that a single person or smaller group will run a site.
IMO I think that you're going to get two groups of poeple emerge from this. One group will just shut down their sites to avoid running a fowl of the rules and the other group will go the "go fuck yourself" route and continue to host anonymously.
Very little legislation does.
Two things my clients have dealt with: VATMOSS and GDPR. The former was fixed with a much higher ceiling for compliance but not before causing a lot of costs and lost revenue to small businesses. GDPR treats a small businesses and non profits that just keep simple lists for people (customers, donors, members, parishioners, etc.) has to put effort into complying even thought they have a relatively small number of people's data and do not use it outside their organisation. The rules are the same as for a huge social network that buys and sells information about hundreds of millions of people.