Sanitation prevents the nasty non-handwashers from contracting the real killers.

Cholera, Scarlett fever, etc. The illnesses that we never hear about.

Sanitation is about more than hand washing. It's running water, water treatment, sewers, sewage treatment, etc.

Also, there's significant evidence that handwashing isn't all that significant in reducing viral transmission.

It's mostly effective in preventing the spread of bacteria.