The benefits of washing your hands depends on a fairly large set of other improvements and inventions.

For most of history the water available was frequently contaminated with human and animal waste, along with whatever your local tanner was dumping in. Fixing that was a prerequisite to making hand washing useful.

And then there is the soap issue. While soap certainly has a long history, it was often unavailable or prohibitively expensive. Cloths were traditionally washed with urine.