Bringing this one back from the dead...
I have recently come to the decision that the position requiring the lowest skill is carry. Think about it, as a carry your primary responsibility is to farm and not die for the first 30 minutes or so, then just clean up the enemy team once you have the requisite items.
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Supports win games.
Supports are important, but not all carries are one-dimensional skill-less heroes.
I agree that not taking one support is a bad idea. But taking like 3 supports is usually a bad idea. And the DOTA 2 'class' naming is usually pretty weak, as a lot of supports usually have 3 to 5 roles, so supports aren't really just supports. Like a lot of supports are also really good nukers or stunners and can be played as semi-carries themselves. Tide-hunter is a support but he's basically a stunner/tank. Jakiro is a support but he's a nuker. Ogre-Magi is not intended to be a support really, but he's pretty easy to play as an item support (Mekansm, Pipe, Urn, got buffs and stuns).
The most one-dimensional carries are picked the most often, and cried about the most often e.g. Drow, Sniper, Ursa, etc... I'd say the 'auto-cast' carries (Drow, Viper, Clinkz) probably require the least skill so those are the ones that people usually cry about. But then there's also 'over-powered' carries---Blood Seeker, Life Stealer, Spirit Breaker, which are pretty easy to skill build with and usually dominate team fights; and they usually get picked up in lots together on the same team. And there's also 'noob' carries that new people are attracted to play (e.g. Ursa, Riki, Medusa) but aren't as easy to play as they initially seem.
Farming on some carries requires skill, and devising an item/skill build for a carry requires some strategy for some carries. Troll Warlord is a farming carry that requires a bit of strategy and skill and is very flexible to build up. Medusa and Ursa require a good bit of farming skill in my book. A lot of players cannot efficiently farm Ursa which can cost the game. And then there's Invoker who is both really simple (about 2 or 3 ways to play it) but also very customizable.
And definitely carries can take part in team fights in some way by about 15 min mark. Usually the lane-ing phase is over by 20 minutes. Medusa is about the only carry I can think of that I dont see team-fighting until late game.