How important is drying hands for sanitation?
If you are immediately going to moisten your hands your hands anyway, I can't see a difference. But otherwise, food safety studies do say that you should thoroughly dry your hands after washing using a clean (or paper) towel.

Decades of research from hygiene authorities suggest that wet hands transfer bacteria much more readily than dry ones, as the residual moisture left on hands after leaving the wash station allows bacteria and viruses to transfer to food and solid surfaces by touch...
Multiple studies have looked at the effectiveness of air dryers versus hand towels and results strongly favor paper towels. For example, one study published by the University of Leeds in 2014 found that levels of airborne germs collected and counted near warm air dryers to be 27 times more than those near paper towel dispensers. Another paper, published in 2012 by the Mayo Clinic Proceedings, which observed research from a dozen investigations, stated that “from a hygiene standpoint, paper towels are superior to electric air dryers” and “should be ­recommended in locations where hygiene is paramount.”

-Food Quality and Safety Magazine (A source of peer-reviewed scholarly articles)