Right, I made a very similar topic asking/ complaining about the lack of recognition Double Battling gets in the competitive world on GameFAQs, so you will excuse me if I just copy & paste it into this topic.
I really don't know why doble battling isn't popular. Is it too complicated for feeble minded Pokemon players? That can't possibly be true, can it? Because double battles could have much higher levels of skill and startegy required. Think of a couple of the situations. You've got something fast that knows Skill Swap/Gastro Acid on your team. You've also got a Slaking. You use Skill Swap/Gastro Acid on your own Slaking, getting rid of Truant and making it much more powerful and USEABLE. If you now have a Pokemon that has Truant (ie you used Skill Swap) you can then swap that onto your opponent and so cripple it or at least force a switch. The possibilities of moves like Skill Swap and Trick in double battles is immense.
Another scenario is Flash Fire + Lava Plume. Having one Pokemon with Lava Plume and one with Flash Fire means you can hit both Pokemon on your opponents team AND boost your other Pokemon's Fire attacks with just one move. A similar thing could be done with Surf + Water Absorb and Discharge + Volt Absorb.
And Guts users could hold other items while having a support Pokemon (that's the term I'm using to describe Pokemon like the ones holding Skill Swap) use Toxic / Will-o-Wisp on you, meaning you can use something like Life Orb or Choice Band for increased power AND without having to wait a turn to set up (so long as the Support Pokemon is faster than the Guts user).
Also, current tactics in 1-on-1 battles like SunnyBeaming would take only one turn to set up rather than 2, meaning the battle would be much more fast-paced.
Also, I hear that Shoddy is going to update and hold double battles soon, so maybe Libelldra could get ready for that by adding a Double Battle board where people can post their movesets for Pokemon for use in double battles? Maybe then we might see the popularity of double battling increase?