This line of thought leads to the sentence immediately following the one you quoted: if there are a large percentage of people who were hesitant due to sincere safety concerns, the mountain of data showing that the vaccines are low-risk will translate into more of them getting vaccinated but if they're motivated by factors which are not affected by scientific data then the primary mechanism for ending the pandemic will be the kinds of requirements which are made possible by full approval. That either gets people vaccinated or removes them from many contexts where they pose risk to everyone else.
Right now there are a lot of concerns raised about vaccine safety on political and social media. Some of those are devout anti-vaccination activists but I believe that they are still a relatively small fraction of the hesitant. When not being vaccinated comes with a direct personal cost we'll see how sincere those beliefs are.
