Wait, what diseases? And are the risks worse than those involved with food preparation or janitorial work (both unlicensed)?
EDIT: Lice, obviously, but that's both treatable and not particularly dangerous.
Here in Washington state you do need a food handlers license just to wash dishes in a restaurant. It's not especially onerous, something like $15 to take a fairly simple test. (And even for the lowest-wage employees I imagine most Restaurants will eat the cost of licensing without complaint.)
And I think it's the general assumption that you don't need to worry about disease in a salon that merits the higher barrier of entry to getting a license than a Janitor, where everyone knows that if there's a bunch of human-sourced fluid on the ground, you need to be careful.
Barbers still use straight razors these days (at least mine does! If yours doesn't, find one that does, it's a treat!), and other implements that can cut you.
