Of course but that's not what authorities and all kinds of pro-vaccination people were saying at the time. General statements about safety don't inspire confidence. There's a possibility that the vaccines are beneficial for some groups but not others, for example.

Even today in my country they do everything possible to coerce people into vaccination. They come just short of abolishing personal freedom and consent. This is not how things are supposed to be done. People should want to take vaccines because there's data that shows benefit. Losing their trust means they won't even trust the data.