For many people, it does prevent getting the virus. My daughter has been repeatedly exposed in her job as a high school nurse, and has tested negative after every close exposure. Unvaccinated teachers and staff, on the other hand, have tested positive after exposure to the same kids, and some have become quite ill.
If you do get a "breakthrough" case - infection in spite of vaccination - you are correct, it generally does lessen the symptoms. That is why 90% plus of hospitalized Covid patients are unvaccinated.
Sue