The virus already is a mild cold for the grand majority of individuals. The statistics over the past 1.5 years demonstrate started this.

But yes, in an ideal world (would never happen for any virus in any population) if every single individual could be and were vaccinated, the diesesse would be effectively eliminated. However, I do not believe the idea that the vaccine doesn't prevent spread. Spreading a respiratory virus requires a person to spread it through bodily fluids usually in the form of sneezing or coughing etc. With no symptoms, chance of spread reaches extreme lows. Smallpox is effectively eliminated because vaccination prevented it's spread so much it "died off" from being unable to spread. It's not like everyone is walking around actively carrying smallpox virus within them.