Pure Elemental Shaman is not bad, but it does have a bit of a slow start. With Quest Rogues becoming more sparse now and Sherazin lists becoming more common, it's not that bad, as the defensive options of pure Elemental Shaman against aggro are still pretty good.
That said, Jade Claws + Jade Lightning package adds more ways for you to interact with the early board as well as some reach, so it seems a desirable addition. And once you add those, Aya Blackpaw comes in naturally. Those five cards are quite affordable without sacrificing Elemental synergies.
Some people also take the next step and add a small Pirate package (typically Patches the Pirate and two copies of Bloodsail Corsair) to add even more early game. You would usually cut Lightning Storm altogether if going for that option. I'm not sure going so far is needed, Elemental Shaman is pretty good at stabilizing.
It's Jades+Elementals guys, the massive tempo swings alloted by Jade Claws, Jade Lightning, Fire Elemental, Blazecaller etc is just so powerful mid game. The only negative synergy between them is Jade Claws on 2 ruining the turn 3 elemental play, but having a weapon to build board advantage is just too important and the fact that it puts something on board is nice too. One way I've found to mitigate the Jade Claws overload issue is to run Fire Fly. Drop Fire Fly turn 1, Jade Claws turn 2, Flame Elemental turn 3. It's not the ideal curve, but it still lets you get out Tol'Vir Stoneshaper on curve, and the weapon is much better for board control than any of our 3 drops early on. It also helps long-term because you can now save Hot Spring Guardian for healing a Stoneshaper/Fire Elemental/Blazecaller later on instead of healing face for 1 on turn 3.
How does it ruin swing turns? Jade Claws and Jade Lightning ARE swing turns. Anything that removes+develops at the same time is insane utility for us. Also from the sounds of it, since you've mentioned Brann, I'm guessing you're using a Jade heavy package with Spirits/Chieftains etc. The only Jades you need are 2x Claws, 2x Lightning, 1x Aya Blackpaw. That's it. Maybe tech in one Jade Chieftain though I've never found the need for them.
I was an Elemental purist but adding Jades really helped my early and mid game. Cheap token minions work well with Firetongue, trade efficiently, and eat removal so my main course of Elemental don't have to. Jades and Elementals are the peanut butter and chocolate of Hearthstone.
This is the current jade elemental shaman i use to ladder, i have a good winrate with it and usually don't have problems with most meta decks. Air elementals are there because a los of classes have trouble to deal with them and i hate mage. Devolve is way more useful than it seems and it can be combined with Kalimos to clear at T10 also it can deal with board that have 2+ deathrattles which is nice against quest priests(which i found a lot more than i thought i would)