So then shouldn't be a problem to stop it entirely, right?
Which laws and which books? I can't find anything.
While (as far as I know) the law was never actually used to ban books (only documentaries), the case became infamous because the government argued that it had the right to ban books if it wanted to. See, e.g., the NYTimes article below: "The [government's] lawyer, Malcolm L. Stewart, said Congress has the power to ban political books, signs and Internet videos, if they are paid for by corporations and distributed not long before an election.".
https://www.nytimes.com/2009/03/25/washington/25scotus.html https://en.wikipedia.org/wiki/Citizens_United_v._FEC https://www.law.cornell.edu/supct/cert/08-205