I'm actually a little puzzled that they're not pushing the Doubles format harder in-game, especially since it's the official format for competitive battling.
You see, the main problem with Singles is that every Pokémon has to pull its own weight. This means that the game favours offensive Pokémon which can defeat the opponent quickly, and heavily disfavours defensive ones. Since you have to backtrack a bit to heal, taking damage at all is a liability. It's no fun having to return to the Poké Center after every battle. Thus, it's better to end the battle without taking damage, than winning by wearing the opponent down. Or put another way: The longer time your Pokémon takes to defeat the opponent, the worse it is. There's also the time aspect itself, it's no fun to spend 20 turns defeating every random trainer by sponging attacks and Toxic-ing. Stall-fests are no fun, no matter how good your Pokémon are at it.
Support Pokémon are rarely seen too. I mean, in some situations moves like Simple Beam, Wide Guard or Helping Hand are awesome. When you're alone on the field, they're the exact opposite. A Pokémon in a Singles support role is entirely dependant on Baton Pass to do its job, and even when it does it well, the supported Pokémon is usually good enough to win the battle without help. The turns spent setting up with one Pokémon and then Baton Passing could have been better spent just dealing damage. The games are too easy for support to be required, and support is hard to pull off effectively anyway.
As such, people tend to disfavour defensive or supportive Pokémon in Singles. Pokémon that don't see use in Singles battles won't gain experience, fall even further below the power curve, and are therefore even more likely to be removed from the team in favour of more offensively-oriented Pokémon. The likes of Audino, Steelix or Shuckle are practically useless since they're judged by their ability to inflict direct damage, rather than the job they do well. In an apparent attempt to offset the inherent advantage of offensive play styles, Game Freak has kept boosting the defensive stats of defensive Pokémon way above what is the norm for offensive stats of offensive Pokémon.
Have a look for yourself. Base 140+ offenses almost exclusively belong to Megas or Legendaries. Random stuff like Torkoal, Onix and Lairon sport defensive stats above 140. There are ten Pokémon with Defense above 180 and five above 200, but only five 'mons with Attack stats above 180 (all of which are "super formes"), and none above the 200 mark. Despite these Defense boosts, though, defensive behemoths remain near-useless unless they also have decent offensive stats.
However... in Doubles it's a different playing field. Suddenly, a Pokémon doesn't have to defeat an opponent directly to gain experience. It's enough that they stay on the field. Support moves help mediocre Pokémon become hard hitters. Defensive 'mons that stay on the field practically forever can be really useful, dishing out status moves while the teammate helps with direct damage. The impressive, but nowadays rarely seen, arsenals of support moves of some Pokémon are actually
good in Doubles, but the games give us so few opportunities to utilize them. So few chances to learn the strategies. So few competent opponents to try them against (most Doubles trainers in the games sport only one set of two Pokémon). And even though they're useful in official competitive battles, actually training a competitive-level defensive or support 'mon is such a chore, since they have to gain Exp. mostly through Singles battles, or hitchhike on the back of the Exp. Share. Ironically enough, a good Doubles Pokémon will have to go through a Singles training regimen in order to become useful.
There's also the inherent issue of the physical/special spectrum, though. A physical offensive Pokémon may never have to use its Sp.Atk, but a physical defensive Pokémon will have to use its Sp.Def, and vice versa. Offensive 'mons dish out damage at the one side of the spectrum they specialize for. Defensive 'mons take damage from both sides, and will crumple like paper if they're too specialized. This simple issue means defensive Pokémon will never be just as good as their offensive counterparts, but either way I believe they would pull their weight a lot better in a Doubles-oriented game than in Singles.