Pelliper is used over Politoed since it has better roles and ability. Why U-Turn? Let's say your opponent switches his opponent to a Drought/Sand Stream/Snow Warning Pokemon. Then, if you don't use U-Turn, the Drizzle would be wasted and you would be spending another turn switching to save your Pokemon. U-Turn is used so that you can bring your Pokemon while seeing what your opponent plans. Another roles. Without Drizzle, Politoed is useless. BST don't matter; it matters what moves and roles a Pokemon has access to. Pelipper also gets Roost, which is reliable recovery. Plus Hurricane with 100% accuracy in rain. Apart from that, he acts as a Defogger since he also gets Defog.
Hope this helps!