It was a problem because initial indicators showed it squashing Beta like a bug. It was just unfortunate that the narrative was then played on too much instead of the actual vaccine effect which is like you say, to reduce infection severity and death. Maybe media were at fault here too?
It also then unfortunately gave the tinfoil brigade ammunition to claim the vaccines are not needed since you could still be infected. Unfortunately those people have tunnel-vision so could not expand their understanding to include the fact that even though you can still be infected the vaccine does help, and will help, and will save you - it just can't promise never to get you infected. Once the pseudo-science is combined with tradition, hocus pocus, belief in aliens and other nonsense you have a very difficult hill to climb to convince people otherwise.