As shigeta touched on, there's no practical way to avoid cross-contamination from other humans. Assuming by magic you delete all your mouth bacteria, there are so many paths to re-inoculation you couldn't avoid it without living in extreme isolation.
A non-exhaustive list of all the ways you could get re-inoculated:
- aerosolized saliva from coughing/sneezing
- eating food exposed to same
- Touching something contaminated then brushing your teeth
- Essentially putting anything another human has touched in your mouth
Other humans get saliva on things they touch and things they breathe on. You can't breathe or eat those things without cooking them. No fresh vegetables.
Your white blood cells or your immune system in general won't help, because S. mutans is already adapted to live in your saliva and there's not (to my knowledge) any adaptive immune system components active in your saliva.