Yes indeed, an unvacinated child is no threat to a vacinated child.
But after the scare about Whooping Cough vacine, 30 years ago the age for vacinating babies was lowered. If every child is vacinated you can afford to wait till the babies are older, and less at rik of side effects.
But it should be a parents choice. By cousin lost a baby after measles vacine, just before my youngest was due to be vacinated so...