Hi. Feeby (15+ yo) didn't do it until just in the past couple of years when she started scooting one of her water dishes toward her before drinking. I changed the water dish to one that wouldn't move, and then she started using her paw to drink from. She doesn't really rest her paw in the water, but certainly has no issues getting it wet enough to drip water on the floor while she is drinking. Oddly enough, she has two other water dishes and for the most part she doesn't do the same thing with them.
While I don't know why she started it, I just chalk it off to another one of those 'cat' things that some do and other don't - pretty much like all the other weird idiosyncrasies of being 'a cat'!!
To quote my father, "Who knows from cats?" Some just seem to love to play in water. It could be worse. She could have become fascinated with watching the toilet flush, and learned how to do it herself! At least this little habit won't shoot your water bill sky-high!