Have ADCs lost their importance?

I've recently (literally, a few days ago) finally bought my 16th champion and jumped right into Ranked.

So, as a typical player, I don't tend to be overly toxic and try to be as game-friendly possible.

I started playing League with my boyfriend a few months ago, back in June as I recall. Since then, I've come to favor the role of AD Carry, and specifically, Ashe. Over these months I've grown into a flexible player who has adjusted to a build of Ashe that is, in most sense, over-powered--with double BF swords early game before any build. And by the end of the game, I have Infinity's Edge, Bloodthirster, and Blade of the Ruined King. I loved Ashe--all I wanted was to play ADC.

But now, I dread playing ADC. I've come to the conclusion that all these toxic supports, bad junglers, and overall poor gameplay of the ADC (I own Sivir and Caitlyn, and really don't like either of them) has turned me away to play other roles. I've played Jinx, and her skill set sets her a little higher than the rest of your typical ADC.

Since the ADC is typically so squishy, I figured they must be able to do so much damage. But anymore I find it to the Mid lane or other melee champions for so much damage, even though Ashe can be a valuable asset to her team for her slows, she isn't much of a carry.

Since the buff of the supports, the old ADCs have so much to live up to. When Sona can out-damage Ashe, I find something wrong. I was in a game where I was Ashe with Leona against a Sona owning the Pentakill skin and Caitlyn as her ADC. The Sona built the gold income items and built the rest AP items. At the end of that game, she done more damage to me than her ADC.

It isn't rare to see a team have no ADC and still easily win a game against a team that does. In a ranked game that I lost yesterday, Alistar and Thresh were Bot Lane. We had Caitlyn and Leona. I was Katarina against Cho'Gath. My team lost so bad, it was pitiful. I feel like the ADC isn't cutting out for Season 4. It's lost its importance in the game, because honestly, you rarely find any ADC that goes Legendary unless your team is just so countered it's terrible.

I even got into a game where Volibear was our ADC, and actually did pretty good.

Even as Ashe, I have to get a support like Thresh or Blitzcrank who have to aid me in the getting the kill before I do any good.

I am concerned to see if the community feels as if the role of ADC isn't really a "carry" anymore or if a buff is needed since the supports got buffed. Please tell me how you feel, I'm so curious to see how League of Legends players feel. I know Ashe isn't one of those "High Damage" champions but even as other champions who are ADC, I feel as if I have to have a Gold League + support to even have a chance. Tell me your opinions! Thank you!