It's strange because it's unhygenic but a strong "social lock in" makes it essentially impossible to abstain without sending the signal of being socially awkward.

As a social construct, there'd be no need for going through the procedure, yet everyone basically has to go through it because everyone else does.

Considering that there are plenty of cultures in which handshakes are not commom (like in many Asian countries), there doesn't seem to be any good justification why it's done elsewhere, other than "custom". But not every custom actually is reasonable.