I find it very difficult to feed soaked feeds. In winter, you have freezing weather to deal with, and in summer, it can go sour very quickly. Makes a slobbery mess which is a pain to clean or attracts more flies or is just a general pain in the butt. Also hauling water around to soak with or carrying soaked feed from the house to the barn is a huge pain if you don’t have the luxury of running water in the barn.
I’ve never actually fed beet pulp, but I have fed many other types of pelleted feed, (High Fat/High Fibre, EasyCube, etc) and never soaked any of them. Too much effort for negligible benefit.
Alfalfa cubes I always soak because they are sometimes huge and hard as rocks.