It won't just be the kids, adults as well, those who can't be vaccinated for legitimate reasons and those whose immunity has gone.

The UK don't vaccinate against chicken pox for a similar reason (namely, most people in the UK have acquired their immunity naturally and get a natural booster through contact with a child at points through their life - introducing the vaccination as one of our regular youth vaccines would remove the natural booster and the impact on older generations who's immunity has waned would outweigh the benefits of vaccinating). Obviously measles isn't chicken pox and should be vaccinated for, just using that as an example.