I still remember another younger kid visiting us, and me telling her mom that I had chickenpox and was probably infectious, and she said that it was fine because her kid was vaccinated - and my reaction "Wait, I could have been vaccinated against this?!"
Our daughter (in the U.S.) got sent home by the school nurse with a single suspected chickenpox sore. She had been vaccinated, and that was her only symptom. No fever, nothing. Buy my wife had never been vaccinated, and never had it as a kid, and she came down with it and it was HORRIBLE.
"Mild" or not, there are also long-term consequences that are decidedly not mild, like shingles...