I went from bronze 3 --> silver 5 in about 110 ranked games playing 98 games with nocturne in the jungle. You don't need to learn multiple positions if you're a jungler or a support even though there will be games here and there that you'll get stuck in spots you're not great at.
Don't get me wrong, I'm not going full ****** if I get stuck in top lane or support. I look up a build for a champ that I want to play, and I've watched enough Dyrus vids to know how to at least be competent in top lane. Support is easy once you have the build and wards spots figured out. (easy to survive, not be amazing.)
I think you'll have more success specializing one role, or even one champion. Just make sure you at least know the mechanics of many.
The rest of what you said I totally agree with though
Why was this down voted? He's completely correct.
The best way to increase elo is through specialization. Also, being able to hit good CS helps a lot. If you try to learn multiple roles you will just end up learning something only to become rusty at what you just finished memorizing.
It's like if you practice landing skill shots for jungle lee sin, only to learn ADC and last hitting. If you go back to jungling with lee sin after days of practicing adc, I can guarantee you you will not be jungling as well as you were prior to playing adc.