A 1% death rate with a disease as contagious as COVID means more than 50 million dead globally at some point (not everyone will get it but the majority will eventually).
Near universal vaccination with a vaccine that is 95% effective at preventing severe cases means saving 47.5 million lives in that scenario. Despite the disease having a 99% survival rate.
If the vaccine provides sterilizing immunity (or just reduces your ability to pass it on), it could save more, and wouldn’t even require universal vaccination to do so.
Furthermore, people are staying home voluntarily in many places. An effective vaccine will alleviate their fears and help the economy. In a way that telling people not to worry about a <1% chance or death will not.