It's just as old a tradition, and it's much harder to hide weapons or recording devices when you're in the buff. If I am vulnerable to being staked through the heart, I will invest in a stake-proof breastplate that I can wear under my normal clothing. If I am vulnerable to holy water, my clothing will be properly waterproofed and I will have an umbrella handy. There's no reason to lie around for centuries until some poor peasant accidentally drips blood on my grave. If I have powers over animals, then I will use those powers discreetly and I will send the animals away after I have no further use for them.
Nothing attracts unwanted attention like a horde of rats invading the neighborhood.
There is no logical reason for someone to mistake another human being for a fifteen-foot bat, not even in hysteria. Therefore, I shall refrain from such transformations in public. I will not give myself away by turning into a bat in climates and seasons where bats don't naturally exist. I also won't do anything that a natural bat wouldn't do, like banging itself against windowpanes and squeaking frantically. If I am revealed as a vampire, I will make a great show of being repelled by something in my environment that I'm not really bothered by, in the hope that this will throw off my attackers.