If it made a significant difference, you should have seen a significantly different outcome in Korea.
People contaminate their hands often within minutes or seconds of washing them.
The major advances in hygeine are due to water treatment, refrigeration and waste management and the ability to not live in total squalor.
Here, some nice person has spelled it out for you.
"Washing hands prevents illnesses and spread of infections to others
Handwashing with soap removes germs from hands. This helps prevent infections because:
People frequently touch their eyes, nose, and mouth without even realizing it. Germs can get into the body through the eyes, nose and mouth and make us sick.
Germs from unwashed hands can get into foods and drinks while people prepare or consume them. Germs can multiply in some types of foods or drinks, under certain conditions, and make people sick.
Germs from unwashed hands can be transferred to other objects, like handrails, table tops, or toys, and then transferred to another person’s hands.
Removing germs through handwashing therefore helps prevent diarrhea and respiratory infections and may even help prevent skin and eye infections.
Teaching people about handwashing helps them and their communities stay healthy. Handwashing education in the community:
Reduces the number of people who get sick with diarrhea by 23-40% 2, 3, 6
Reduces diarrheal illness in people with weakened immune systems by 58% 4
Reduces respiratory illnesses, like colds, in the general population by 16-21% 3, 5
Reduces absenteeism due to gastrointestinal illness in schoolchildren by 29-57% 7
Not washing hands harms children around the world
About 1.8 million children under the age of 5 die each year from diarrheal diseases and pneumonia, the top two killers of young children around the
world 8.
Handwashing with soap could protect about 1 out of every 3 young children who get sick with diarrhea 2, 3 and almost 1 out of 5 young children with respiratory infections like pneumonia 3, 5.
Although people around the world clean their hands with water, very few use soap to wash their hands. Washing hands with soap removes germs much more effectively 9.
Handwashing education and access to soap in schools can help improve attendance 10, 11, 12.
Good handwashing early in life may help improve child development in some settings 13."
As for a different outcome in Korea, I'd like to see some proof.