This is true, and it is one of the reasons ─ not the only reason, but one of the reasons nevertheless ─ why I chose not to get the vaccine. (My other reasons are medical in nature. I have autoimmune issues, and the vaccine could make those worse, plus that getting the vaccine does not stop anyone from continuing to spread the virus, and that I myself am not an infection hazard because I barely ever go out the door.)
Large-scale vaccination is necessary, but not in the industrialized, collectivist way it has been happening here. There are people who knew in advance that their bodies would react negatively to one type of vaccine but not to a vaccine from another manufacturer, but those people were not given a choice ─ it was either the vaccine that would be harmful to them or no vaccine at all. And if they then opted to not get the vaccine, then they were put on a list of anti-vaxxers.
Shame on the government, but then again, they've been fucking up since this whole pandemic started. First they responded way too slow and they goofed up in acquiring masks and test kits. Then when the lockdown became necessary, they allowed the lobbies to convince them to relax things way too soon, and certain events ─ e.g. sports events and certain cultural events, so long as there was enough money involved ─ were exempt from the lockdown rules and even from the social distancing and from the prohibition on large gatherings, which boggles the mind. The result was a second wave, then a third wave, and now we're already looking at a fourth wave coming in, because they keep on fucking up.