Th reason they banned the two is because the fish got to slippery in rain. None of the attacks made by opposing Pokemon really made an impact on the slippery fish, and also left residue on whatever the opposing used on the slippery fish.
It's like punching soap when you're in the shower, not very effective at all.
My jackassery aside, Smogon is using Aldaron's proposal to test rain. (I believe) Since the two when on the same team, dominated, he proposed they would be split. To see if it was Drizzle that was making rain teams broken, or swift swim.
If Drizzle by itself is proven to not be broken then Swift Swim will see a ban, and if the opposite proves to be true, then Drizzle will be banned.
That's about all there is to it.
"Oh, Mayl..mrph... I am your captain" - Lan Hikari (Megaman Battle Network 2)
Permanent rain makes Pokemon with Swift Swim be faster, and their water type moves are 50 % stronger too. Not only that, Hydration, Dry Skin and Rain Dish also benefit from rain. Without Drizzle, at least you have to set-up for the rain, which will last for 8 turns at most.
I think the same thing should apply to Drought+Chlorophyill and Sand Stream+Sand Throw.