If anything, the game is less snowbally than it used to. Go back to S2-S3 and watch what snowballing means.
Not to mention you say that "I'd prefer it if I felt like I had SOME effect on my games", which is partly accomplished by ... snowballing yourself. Nothing prevents you from being the one to snowball. " you can snowball off the dumbest things, like the enemy making a mistake" is ... normal ? Being better than your opponent should give you an edge.
Also you do have impact on your games. The percent of game that cannot be won due to your team is maybe around 20%. But that's it.
I got 3 accounts to diamond, each by playing different roles (mid, jungle, top). And guess what ? I still climbed with a 80% winrate up to plat, and then finishing at 65% in diamondV, regardless being wrongly placed in silverIV on one of my accounts.
You are the only common factor in your games, if you are not winning, it just means that there are some parts of the game you haven't mastered yet.
So when you say that a great deal of the game "has to do with things that have very little to nothing to do with your personnal skill", I have to disagree strongly. How you react to having your botlane get killed is also part of your "skill".
Many low elo players who talk about their "skill" refer to the way they play in lane and teamfight. And sure, being good at both will get you somewhere around gold elo. But knowing when to roam, when not to trade, how to mentally keep track of the ennemy jungler, how to splipush correctly (and not just push alone and die), how use your positioning in lane to force the ennemy positionning, how to manage the minions waves, etc. are the kind of things that people very often don't take into consideration, because it's a kind of "passive" skill, so to speak. It's not doing a sick flash combo to kill the opponent, it's playing slow and calculated, freezing the wave, denying cs, getting a 30 minions lead on your opponent ... and you're up a kill in gold, except you never killed your opponent, and now you are ahead. But it's not flashy, not epic enough, so people forget about that, or just don't know how to pull it off properly.
Low elo players don't know what they don't know (seems pretty obvious doesn't it ?) which is why there is this "it's just being unlucky" explanation. When in fact you could have changed the way things went, but you just didn't know yet how to.