There's a reason that this is the setup that pros use. It's designed so that you have a good mix of damage types and sustain. Mid provides ap burst, the marksman provides ad burst, top or jungle usually provide sustain because they're tanks. The support is there usually to provide an interrupt or other cc of some kind. I'm not saying it's perfect, and that it doesn't fall apart if someone feeds, but it usually does what it's supposed to.
That being said, each role has a job, and I'm not always certain that everyone knows what those jobs are.
Junglers are mainly there to secure objectives and occasionally help you win lane, and in that order. Their priority is making sure that your team gets the objectives, not just the kills. Kills are good and can lead to better objective control, but too many people don't use their gold advantage to get objectives.
The reason bot lane is ADC and a support is because the ADC is very squishy, and marksmen have the highest late game output, so it's best to get them fed as much as possible as quickly as possible. You also don't want to run a solo lane against a duo lane. Go ahead, try telling your support to go help mid when you're Vayne trying to take on Blitz and Graves. You won't have a good time unless the other team is vastly inferior to you.
The reason that there's only one person on mid and top is because a) that's who's left over, and b) it helps take advantage of all sources of gold on the map. That's another responsibility of the jungler, to get gold advantage from the spawning jungle creeps without affecting the income of the people in lane. The reason that certain types of champions are chosen for certain kinds of positions on the map is deliberate as well. Bursty caster champions go mid because it's shorter than the other two lanes and you can easily take your damage to either of the other lanes via roaming. Also, if you die, you have less ground to cover to get back into the game. Top is usually given to a tank because tanks are supposed to have high sustain, high survivablity and generally go back to base less often. The two on bot lane are there because, with two of you, you can better protect each other.
I hope I've made it clear why things are the way they are; with this knowledge, I hope that you'll see better what each role should do and why, and maybe make you a better player in the process (because I presume you didn't know this to begin with). Most players don't necessarily understand this, and that's why many games fall apart at lower elo, and those problems with "feeders" you seem to be having probably extend from this or lack of technical skill. The way you can make up for this is to be the person that can carry a game by yourself. In most cases, you're probably not using this setup correctly. For instance, you can trace back why you lost and what you may have been able to do to stop it. If you're mid and you lose, you might go, "I lost because top lane fed." Then you can go back and ask yourself: "Could I have stopped that from happening?" The answer may very well be yes. If you're mid, why didn't you roam? Most midlaners have a way to push lane in their kit, so you could have probably pushed the wave and helped top out if they were struggling. Don't always do this because sometimes there really is nothing you can do to help, or providing this help would ultimately cause more damage than good (e.g. you can't push a wave, and you're pinned down to your tower; towers are objectives and objectives are more valuable than kills).
