The danger is higher - that's exactly why we do it. It's an easy way to create intimacy with a stranger quickly. There's a reason politicians shake hands and kiss babies.

Handshakes far predate modern germ theory of disease. The "danger" doesn't really help with intimacy in any way. It's completely unnecessary danger. We'd find sharing tissues with strangers to be disgusting if it were introduced as a greeting today, but touching the hands of someone right after they've sneezed and coughed into them--after which we often unknowingly touch our own face--is regarded as a sign of intimacy or respect.

> We'd find sharing tissues with strangers to be disgusting if it were introduced as a greeting today

Sounds like you're unfamiliar with the practice of agreeing to a deal by both parties spitting into their hand and then clasping hands?

There's also the idea of making a pledge by both parties cutting their hands and then clasping hands, mixing blood with each other.

When was the last time you saw anyone do either of those things, other than in a movie?

I've never seen anyone bow in greeting outside a movie either. (Assuming we're considering books to be "movies".)