I've read that these "childhood illnesses" are not so bad if you get them as a child. For example, the cut-off for chicken pox parties among the natural moms who still look for those is known to be 12, because the immune system changes (matures) around 12. If you get chicken pox after that, it is even more uncomfortable with longer recovery. And you definitely don't want to get it as an adult since it can turn into the dreaded shingles.

The chicken pox vax is still somewhat new, and apparently it is being discovered that it "wears off" sooner than expected, requiring more boosters.

So your choices for kids are: get a series of shots every few years which many moms don't want, get no shots and risk catching it as a teen or an adult, or deal with the illness as a kid (which sucks, yes) and have lifetime immunity.

I don't know off the top of my head if measles is similar with the 12 year rule of thumb. None of the non-vax moms I know have it on their radar, so it's not discussed like chicken pox. I would only assume it's similar philosophy -- get lifetime immunity as a child since it's a childhood illness.