Reading a lot of VGC war stories, I've noticed that people do attempt to counter-pick often, with varying results. The best players seem to be able to guess what threats their opponent will prepare for and attempt to exploit their resulting team building. I therefore think that counter-picking, while a difficult and often counterproductive skill to master, is something that is worth learning at higher levels of skill.
I think one example is Bisharp when you see a landorus-t on the other team. In my latest Nugget Bridge Major game, I ran a team with Bisharp and my opponent had a Lando. Normally, the threat of leading Bisharp stops your opponent from leading Lando, so I left Bisharp behind, and it paid off (he led Kang, a surefire Bisharp killer). Game 2, I guessed my opponent would be a little less hesitant to lead with Lando, so I brought Bisharp as my lead, and it paid off again.
On the other hand, when trying to counter pick, there's a balance between getting the best possible lead match-up and playing it safe. Ideally, you'd pick two pokemon which could together counter any combination of two opponents. If you predict your opponent is going to lead with two pokemon, you'd have an idea of two pokemon which can beat it. If they don't have any glaring weaknesses, then its probably a good idea to bring them, but if your opponent would gain a significant advantage over that combo with a different lead match-up, perhaps it'd be better to play it safe.
Of course, playing against a good-stuffs team is very different from playing against a themed team. If you're playing against a rain team, you might be at a significant advantage if your opponent doesn't lead with politoed. Same with TR and Cress/Gothitelle/etc. Leading with the assumption that one of your opponents leads will be the set-up isn't a bad idea, simply because even if they don't lead with it, they're putting themselves at a disadvantage. Of course, a well made TR or rain team would have a non-TR/rain mode, so this isn't as much of an issue, but even then, they still prefer to put themselves in their arena of choice with their lead.