People will disagree, but I'd always prefer to have a strong carry/weak support instead of a weak carry/strong support.
Unless we are talking about "complete idiot" levels of "weak", a strong support can and will carry his bot AD through the laning phase. A player who is mechanically sound (understands last hitting, doesn't overextend), who is "weak" in that he misses a few kill opprotunities... well, with a good support he'll stay up with CS. A good support creates those kill opportunities in the first place. They aren't happening unless your opponents make a grave mistake or your jungler gets a gank. The AD carry simply isn't going to be doing many initiates at level 3. (initiates != poke).
Good supports control the bush, waste junglers times, secures dragons by winning the lane, zones the enemy AD carry.
Think of it this way:
A strong support, with a weak carry is 1.5 people, and ensures the enemy stays as 1.5 people. End game, they become like 1.25 people (initially carry is .5 person, later support = .5 people)
A weak support, with a strong carry is 1 person, and does nothing to keep the enemy down. End game, they become 1.25 people (initially, carry is .75 people support = .25 person).
A strong support will prevent their team from face-checking baron and getting aced in the first place, so that their carry can even get the chance to shine.
Then consider the placement in picking. If I'm in the top 1 or 2 slot, I can still call and, more or less, demand what role I will play.
To be fair, you do that when we play in-house games too.
For all you know, he's just awful and will lose you the game. Better to trust yourself to a more important role than to relegate it to someone else and hope they aren't awful. Eg - going support in a pug means you are boned if your lane mate is rubbish. And you don't know if you lane mate is rubbish unless you're duo queued with them. So, its best to take a carry or jungle role imo. Then you rely on your skills at least for your lane.
i think that this only applies if you're playing someone who you are familiar with, you're good with, and you're "Tryharding". (i understand you're talking about ranked here - you probably tryhard more in ranked, but this is normals).
If you're playing a role/person who you only have a handful of games with, following a guide and buying bad items (like rushing Ninja Tabi's and Madred's Razor (rather than Mecury + Vampiric) against Rumble + Fiddle Jungle + AP mid), then, really, you're putting yourself at a high level there. Someone else could have played that role equally or better than you.
Some noob counter picks, pushes like there's no tomorrow, and gets his ass ganked over and over.
Knowledge of the game != Good technical skills.
It's true until you are higher ELO, playing someone you're more comfortable with (but a weak pick) is going to work out better for you than a natural hardcounter. But the fact of the matter is, if the person picks a counterpick, then pushes the lane, they would have pushed the lane with anyone else.
and then three shot the poor bastard every time your R comes off cd.
isn't that why he is considered a counter? Nearly every other AP pick it'd be one-shot.
i do think that picking "safe" tops (such as GP / Warwick / Lee Sin) that can also jungle, first or second is hardly a big deal. Just like first-picking Kennen or Vlad. Hell, with Kennen you can even AD bot if you "must". Picking champions that really can only play in one lane first or second is putting your entire team at risk, and putting a lot of silly stress on your jungler.
A jungler can and should be able to help one counterpicked lane (afterall, it only makes sense that all three lanes would be even, or one team has a counterpick advantage in top, the other in mid). However, if both mid and top are counterpicked, then that lets the enemy jungler spend some time on bot instead (until you pressure a lane and force him elsewhere). That can spin your bot lane out of control and then you've got even more places to be. If bot is being safe, he can always just farm.
"Pressuring" bot lane can be as simple as him farming a bit longer, and getting an early Oracles and forcing your support to burn a billion wards, plus keeps bot scared.