You are correct in that their exposure to disease is reduced. However, most childhood disease is relatively minor and only severely impacts those who have weakened immune systems to begin with.
I contracted most of those illnesses we now regularly innoculate against. I have to tell you, they were nothing but annoyances that never even resulted in the administration of antibiotics to "cure".
I was regulary innoculated for Typhoid and Rocky Mountain Spotted Fever. These are diseases that don't even cause a blip on the childhood disease radar screens of our present time.
I did the whole childhood illness thing too. Measles- German and 3 day, mumps, chickenpox etc. Not only did I survive, but I am very healthy today. My mother believed that you vaccinated for the big stuff, Polio and Smallpox, but other than that what didn't kill you made you stronger.
She also encouraged me to play in the dirt, which according to my wife would have horrified mothers of 10-15 years ago.