It will take a long time to vaccinate a substantial number of Americans with any COVID vaccine, so having some people wait out the first two or three rounds until they are satisfied that it is safe enough for them to feel comfortable won't make make much difference.
What will make a difference is that without having been infected or vaccinated, you are still capable of getting COVID and passing it on to others whether or not you are seriously ill.
The question is, are you willing to keep wearing a mask and practice social distancing in order to prevent others from getting COVID?
Even when the vaccine is available to 10%. or even 40% of the population, there are plenty of susceptible people out there that can get seriously ill or die if they catch COVID.