Not quite right. Smallpox is not contagious until a rash appears. This is 24-48 hours after the onset of fever, abdominal pain, etc. You are pretty sick before you are contagious.
I am a parent and I can verify that lots of sick, feverish kids get sent to school because no one is home to care for them. Smallpox would spread faster than wildfire.
And those of us with older vaccinations would not necessarily be immune
Booster shots are recommended every 10 years. Us old folks might have a little protection, but don’t count on it. (I got my vaccination, but I guess that I missed out on the boosters.)